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Simplifying x2 + -62x + -90 = 0 Reorder the terms: -90 + -62x + x2 = 0 Solving -90 + -62x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -62x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -62x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -62x + x2 = 0 + 90 -62x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -62x + x2 = 90 The x term is -62x. Take half its coefficient (-31). Square it (961) and add it to both sides. Add '961' to each side of the equation. -62x + 961 + x2 = 90 + 961 Reorder the terms: 961 + -62x + x2 = 90 + 961 Combine like terms: 90 + 961 = 1051 961 + -62x + x2 = 1051 Factor a perfect square on the left side: (x + -31)(x + -31) = 1051 Calculate the square root of the right side: 32.419130155 Break this problem into two subproblems by setting (x + -31) equal to 32.419130155 and -32.419130155.Subproblem 1
x + -31 = 32.419130155 Simplifying x + -31 = 32.419130155 Reorder the terms: -31 + x = 32.419130155 Solving -31 + x = 32.419130155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = 32.419130155 + 31 Combine like terms: -31 + 31 = 0 0 + x = 32.419130155 + 31 x = 32.419130155 + 31 Combine like terms: 32.419130155 + 31 = 63.419130155 x = 63.419130155 Simplifying x = 63.419130155Subproblem 2
x + -31 = -32.419130155 Simplifying x + -31 = -32.419130155 Reorder the terms: -31 + x = -32.419130155 Solving -31 + x = -32.419130155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = -32.419130155 + 31 Combine like terms: -31 + 31 = 0 0 + x = -32.419130155 + 31 x = -32.419130155 + 31 Combine like terms: -32.419130155 + 31 = -1.419130155 x = -1.419130155 Simplifying x = -1.419130155Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.419130155, -1.419130155}
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