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Simplifying 0 = x2 + -62x + -14950 Reorder the terms: 0 = -14950 + -62x + x2 Solving 0 = -14950 + -62x + x2 Solving for variable 'x'. Combine like terms: 0 + 14950 = 14950 14950 + 62x + -1x2 = -14950 + -62x + x2 + 14950 + 62x + -1x2 Reorder the terms: 14950 + 62x + -1x2 = -14950 + 14950 + -62x + 62x + x2 + -1x2 Combine like terms: -14950 + 14950 = 0 14950 + 62x + -1x2 = 0 + -62x + 62x + x2 + -1x2 14950 + 62x + -1x2 = -62x + 62x + x2 + -1x2 Combine like terms: -62x + 62x = 0 14950 + 62x + -1x2 = 0 + x2 + -1x2 14950 + 62x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 14950 + 62x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14950 + -62x + x2 = 0 Move the constant term to the right: Add '14950' to each side of the equation. -14950 + -62x + 14950 + x2 = 0 + 14950 Reorder the terms: -14950 + 14950 + -62x + x2 = 0 + 14950 Combine like terms: -14950 + 14950 = 0 0 + -62x + x2 = 0 + 14950 -62x + x2 = 0 + 14950 Combine like terms: 0 + 14950 = 14950 -62x + x2 = 14950 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 = 14950 + 961 Reorder the terms: 961 + -62x + x2 = 14950 + 961 Combine like terms: 14950 + 961 = 15911 961 + -62x + x2 = 15911 Factor a perfect square on the left side: (x + -31)(x + -31) = 15911 Calculate the square root of the right side: 126.138812425 Break this problem into two subproblems by setting (x + -31) equal to 126.138812425 and -126.138812425.Subproblem 1
x + -31 = 126.138812425 Simplifying x + -31 = 126.138812425 Reorder the terms: -31 + x = 126.138812425 Solving -31 + x = 126.138812425 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 = 126.138812425 + 31 Combine like terms: -31 + 31 = 0 0 + x = 126.138812425 + 31 x = 126.138812425 + 31 Combine like terms: 126.138812425 + 31 = 157.138812425 x = 157.138812425 Simplifying x = 157.138812425Subproblem 2
x + -31 = -126.138812425 Simplifying x + -31 = -126.138812425 Reorder the terms: -31 + x = -126.138812425 Solving -31 + x = -126.138812425 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 = -126.138812425 + 31 Combine like terms: -31 + 31 = 0 0 + x = -126.138812425 + 31 x = -126.138812425 + 31 Combine like terms: -126.138812425 + 31 = -95.138812425 x = -95.138812425 Simplifying x = -95.138812425Solution
The solution to the problem is based on the solutions from the subproblems. x = {157.138812425, -95.138812425}
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