(x-7)^2=1

{ "query": { "display": "$$\\left(x-7\\right)^{2}=1$$", "symbolab_question": "EQUATION#(x-7)^{2}=1" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Equations", "subTopic": "Quadratic", "default": "x=8,x=6", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\left(x-7\\right)^{2}=1{\\quad:\\quad}x=8,\\:x=6$$", "input": "\\left(x-7\\right)^{2}=1", "steps": [ { "type": "step", "primary": "For $$\\left(g\\left(x\\right)\\right)^{2}=f\\left(a\\right)$$ the solutions are $$g\\left(x\\right)=\\sqrt{f\\left(a\\right)},\\:\\:-\\sqrt{f\\left(a\\right)}$$" }, { "type": "interim", "title": "Solve $$x-7=\\sqrt{1}:{\\quad}x=8$$", "input": "x-7=\\sqrt{1}", "steps": [ { "type": "step", "primary": "Apply rule $$\\sqrt{1}=1$$", "result": "x-7=1" }, { "type": "interim", "title": "Move $$7\\:$$to the right side", "input": "x-7=1", "result": "x=8", "steps": [ { "type": "step", "primary": "Add $$7$$ to both sides", "result": "x-7+7=1+7" }, { "type": "step", "primary": "Simplify", "result": "x=8" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7vi6QEw38sRDYhrVqkO/1lpN1pXT08zEQpn0WJ6CFMXCGlgVged/+9z7Z2eY8DdEVIv3pLYfKyQbKCshhkaZHUVB+7aDm7YcruXbrgKP9F1iJLbrsy9PUkt1PkbIMRxhVzPywKoVbgpEyLnOm1p35SGoNVcfQseZgP9DflvaHk8ppN4p8BRvB4Z6NND7NEeC7vihf9GJ/RDUpv7WDe9dh2BeroAIJtrLk5lMET/UWcttPSS3nfYksP2xJ6IVxiM8E16E1dTX6gDXtu7aV9pSVeQwKAu7Z3tN/RgLPjlzyRw8i5OoNNprqQV2UgQUGESqFlvjhqQs5XJJkHv2GQUE6glcrAOsROfiVgP+wtWyh0afthvwKEoR3ksHNHbCkrb6kcwDIfxbr/Pq2vWjsXBdpmP+Gc7uNDn5rFMiDyv69niKS9nJYJSn323kBOgLLJJSHA0M2fLxChFzxWuRIFJwDCn9YihiGR/khifj29p6+pso=" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve Title 1Eq" } }, { "type": "interim", "title": "Solve $$x-7=-\\sqrt{1}:{\\quad}x=6$$", "input": "x-7=-\\sqrt{1}", "steps": [ { "type": "step", "primary": "Apply rule $$\\sqrt{1}=1$$", "result": "x-7=-1" }, { "type": "interim", "title": "Move $$7\\:$$to the right side", "input": "x-7=-1", "result": "x=6", "steps": [ { "type": "step", "primary": "Add $$7$$ to both sides", "result": "x-7+7=-1+7" }, { "type": "step", "primary": "Simplify", "result": "x=6" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve Title 1Eq" } }, { "type": "step", "primary": "The solutions to the quadratic equation are:", "result": "x=8,\\:x=6" } ], "meta": { "solvingClass": "Equations", "practiceLink": "/practice/quadratic-equations-practice", "practiceTopic": "Quadratic Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "(x-7)^{2}-1" }, "showViewLarger": true } }, "meta": { "showVerify": true } }