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Simplifying x2 + -62x + 368 = 0 Reorder the terms: 368 + -62x + x2 = 0 Solving 368 + -62x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-368' to each side of the equation. 368 + -62x + -368 + x2 = 0 + -368 Reorder the terms: 368 + -368 + -62x + x2 = 0 + -368 Combine like terms: 368 + -368 = 0 0 + -62x + x2 = 0 + -368 -62x + x2 = 0 + -368 Combine like terms: 0 + -368 = -368 -62x + x2 = -368 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 = -368 + 961 Reorder the terms: 961 + -62x + x2 = -368 + 961 Combine like terms: -368 + 961 = 593 961 + -62x + x2 = 593 Factor a perfect square on the left side: (x + -31)(x + -31) = 593 Calculate the square root of the right side: 24.351591324 Break this problem into two subproblems by setting (x + -31) equal to 24.351591324 and -24.351591324.Subproblem 1
x + -31 = 24.351591324 Simplifying x + -31 = 24.351591324 Reorder the terms: -31 + x = 24.351591324 Solving -31 + x = 24.351591324 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 = 24.351591324 + 31 Combine like terms: -31 + 31 = 0 0 + x = 24.351591324 + 31 x = 24.351591324 + 31 Combine like terms: 24.351591324 + 31 = 55.351591324 x = 55.351591324 Simplifying x = 55.351591324Subproblem 2
x + -31 = -24.351591324 Simplifying x + -31 = -24.351591324 Reorder the terms: -31 + x = -24.351591324 Solving -31 + x = -24.351591324 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 = -24.351591324 + 31 Combine like terms: -31 + 31 = 0 0 + x = -24.351591324 + 31 x = -24.351591324 + 31 Combine like terms: -24.351591324 + 31 = 6.648408676 x = 6.648408676 Simplifying x = 6.648408676Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.351591324, 6.648408676}
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