x^2=361

{ "query": { "display": "$$x^{2}=361$$", "symbolab_question": "EQUATION#x^{2}=361" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Equations", "subTopic": "Quadratic", "default": "x=19,x=-19", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$x^{2}=361{\\quad:\\quad}x=19,\\:x=-19$$", "input": "x^{2}=361", "steps": [ { "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{361},\\:x=-\\sqrt{361}" }, { "type": "interim", "title": "$$\\sqrt{361}=19$$", "input": "\\sqrt{361}", "steps": [ { "type": "step", "primary": "Factor the number: $$361=19^{2}$$", "result": "=\\sqrt{19^{2}}" }, { "type": "step", "primary": "Apply radical rule: $$\\sqrt{a^2}=a,\\:\\quad\\:a\\ge0$$", "secondary": [ "$$\\sqrt{19^{2}}=19$$" ], "result": "=19" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7/78Vst+IERnYPWyHG4Yaxt6GQqufR6tr2vPxOUv7H+9WJ8nxV0qzaT8AiVuYi7nzhj6ylSwHjJkmQPKH34+7f5aF++KSQCHEhxUyu7VOvk4=" } }, { "type": "interim", "title": "$$-\\sqrt{361}=-19$$", "input": "-\\sqrt{361}", "steps": [ { "type": "step", "primary": "Factor the number: $$361=19^{2}$$", "result": "=-\\sqrt{19^{2}}" }, { "type": "step", "primary": "Apply radical rule: $$\\sqrt{a^2}=a,\\:\\quad\\:a\\ge0$$", "secondary": [ "$$\\sqrt{19^{2}}=-19$$" ], "result": "=-19" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s75D8NS8uIwdaRgBR8G4ukaFXTSum/z5kLpMzXS1UJIezVMYp0lKFnTbVhW8nzy48RCXP3HRkwvQo8XuRFa/NQF1Jh30/IjFmIbj1xagHO700kt3WiGR7ZaCaXvz77bMjS" } }, { "type": "step", "result": "x=19,\\:x=-19" } ], "meta": { "solvingClass": "Equations", "practiceLink": "/practice/quadratic-equations-practice", "practiceTopic": "Quadratic Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "x^{2}-361" }, "showViewLarger": true } }, "meta": { "showVerify": true } }