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Simplifying 4 = x2 + -62x Reorder the terms: 4 = -62x + x2 Solving 4 = -62x + x2 Solving for variable 'x'. Reorder the terms: 4 + 62x + -1x2 = -62x + 62x + x2 + -1x2 Combine like terms: -62x + 62x = 0 4 + 62x + -1x2 = 0 + x2 + -1x2 4 + 62x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4 + 62x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -62x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -62x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -62x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -62x + x2 = 0 + 4 -62x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -62x + x2 = 4 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 = 4 + 961 Reorder the terms: 961 + -62x + x2 = 4 + 961 Combine like terms: 4 + 961 = 965 961 + -62x + x2 = 965 Factor a perfect square on the left side: (x + -31)(x + -31) = 965 Calculate the square root of the right side: 31.064449134 Break this problem into two subproblems by setting (x + -31) equal to 31.064449134 and -31.064449134.Subproblem 1
x + -31 = 31.064449134 Simplifying x + -31 = 31.064449134 Reorder the terms: -31 + x = 31.064449134 Solving -31 + x = 31.064449134 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 = 31.064449134 + 31 Combine like terms: -31 + 31 = 0 0 + x = 31.064449134 + 31 x = 31.064449134 + 31 Combine like terms: 31.064449134 + 31 = 62.064449134 x = 62.064449134 Simplifying x = 62.064449134Subproblem 2
x + -31 = -31.064449134 Simplifying x + -31 = -31.064449134 Reorder the terms: -31 + x = -31.064449134 Solving -31 + x = -31.064449134 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 = -31.064449134 + 31 Combine like terms: -31 + 31 = 0 0 + x = -31.064449134 + 31 x = -31.064449134 + 31 Combine like terms: -31.064449134 + 31 = -0.064449134 x = -0.064449134 Simplifying x = -0.064449134Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.064449134, -0.064449134}
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