5x^2-90=10+4x^2

{ "query": { "display": "$$5x^{2}-90=10+4x^{2}$$", "symbolab_question": "EQUATION#5x^{2}-90=10+4x^{2}" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Equations", "subTopic": "Quadratic", "default": "x=10,x=-10", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$5x^{2}-90=10+4x^{2}{\\quad:\\quad}x=10,\\:x=-10$$", "input": "5x^{2}-90=10+4x^{2}", "steps": [ { "type": "interim", "title": "Move $$90\\:$$to the right side", "input": "5x^{2}-90=10+4x^{2}", "result": "5x^{2}=4x^{2}+100", "steps": [ { "type": "step", "primary": "Add $$90$$ to both sides", "result": "5x^{2}-90+90=10+4x^{2}+90" }, { "type": "step", "primary": "Simplify", "result": "5x^{2}=4x^{2}+100" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s74pnWDu/HeHOrwj4GlNiWdYiYgU4FuqXXXS+GYNc20w8cq+198vCBI10fBUVn6cIf5eFj7HqdClc+p2SsxMdws+3Q8ssxbhbEPwmspnWk6LG/rTugQNmn5yPF0CKNsJQoZTAHbS1UqRpIHIgTS9vS1U+hPmfpWBX0agJ0NurA75wsLWL/oGD++Wi02XE+yuCd3OvvzZUFdU2aUsFW7TB7iexFGHS89JQVGjwXiYovIlT3/LA2SSaqOGlQ8tRH7BTVTxiuZJF6Oi5XpwWE3BNQwNTcoBjiQMeKUzqvjloxiaFFPoW8imL5Ihzz6jeBHy3Vi126KflIGXPj0T66SV3pmAInWVDUUDBWNHqYNa25MfkOAOWTWL/jIC0Sf89wVXjAo3oe/oyhMy2+1TQhDBd2f7idt2RlK9fm/Lt9P6mH3WC6LBtT4H6f7c74IgzFg/ox2oea1dT8rJycbEDAqgbDcA==" } }, { "type": "interim", "title": "Move $$4x^{2}\\:$$to the left side", "input": "5x^{2}=4x^{2}+100", "result": "x^{2}=100", "steps": [ { "type": "step", "primary": "Subtract $$4x^{2}$$ from both sides", "result": "5x^{2}-4x^{2}=4x^{2}+100-4x^{2}" }, { "type": "step", "primary": "Simplify", "result": "x^{2}=100" } ], "meta": { "interimType": "Move to the Left Title 1Eq", "gptData": "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" } }, { "type": "step", "primary": "For $$x^{2}=f\\left(a\\right)$$ the solutions are $$x=\\sqrt{f\\left(a\\right)},\\:\\:-\\sqrt{f\\left(a\\right)}$$" }, { "type": "step", "result": "x=\\sqrt{100},\\:x=-\\sqrt{100}" }, { "type": "interim", "title": "$$\\sqrt{100}=10$$", "input": "\\sqrt{100}", "steps": [ { "type": "step", "primary": "Factor the number: $$100=10^{2}$$", "result": "=\\sqrt{10^{2}}" }, { "type": "step", "primary": "Apply radical rule: $$\\sqrt{a^2}=a,\\:\\quad\\:a\\ge0$$", "secondary": [ "$$\\sqrt{10^{2}}=10$$" ], "result": "=10" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7RW6oBYmo5Js74GBIV6upv96GQqufR6tr2vPxOUv7H+8Khqe7+dajLA9h/DZSrCk/hj6ylSwHjJkmQPKH34+7f95LNcObF6QhiI8u0x4Pxok=" } }, { "type": "interim", "title": "$$-\\sqrt{100}=-10$$", "input": "-\\sqrt{100}", "steps": [ { "type": "step", "primary": "Factor the number: $$100=10^{2}$$", "result": "=-\\sqrt{10^{2}}" }, { "type": "step", "primary": "Apply radical rule: $$\\sqrt{a^2}=a,\\:\\quad\\:a\\ge0$$", "secondary": [ "$$\\sqrt{10^{2}}=-10$$" ], "result": "=-10" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s73Yo/TWK3+US+gViT/5yHB1XTSum/z5kLpMzXS1UJIewogZYyP6viKuQt0bEoFXamCXP3HRkwvQo8XuRFa/NQF7p2tcEzgcG5irjhoZ9/deckt3WiGR7ZaCaXvz77bMjS" } }, { "type": "step", "result": "x=10,\\:x=-10" } ], "meta": { "solvingClass": "Equations", "practiceLink": "/practice/quadratic-equations-practice", "practiceTopic": "Quadratic Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "5x^{2}-90-10-4x^{2}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }