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Simplifying 0 = x2 + -59x + 588 Reorder the terms: 0 = 588 + -59x + x2 Solving 0 = 588 + -59x + x2 Solving for variable 'x'. Combine like terms: 0 + -588 = -588 -588 + 59x + -1x2 = 588 + -59x + x2 + -588 + 59x + -1x2 Reorder the terms: -588 + 59x + -1x2 = 588 + -588 + -59x + 59x + x2 + -1x2 Combine like terms: 588 + -588 = 0 -588 + 59x + -1x2 = 0 + -59x + 59x + x2 + -1x2 -588 + 59x + -1x2 = -59x + 59x + x2 + -1x2 Combine like terms: -59x + 59x = 0 -588 + 59x + -1x2 = 0 + x2 + -1x2 -588 + 59x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -588 + 59x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 588 + -59x + x2 = 0 Move the constant term to the right: Add '-588' to each side of the equation. 588 + -59x + -588 + x2 = 0 + -588 Reorder the terms: 588 + -588 + -59x + x2 = 0 + -588 Combine like terms: 588 + -588 = 0 0 + -59x + x2 = 0 + -588 -59x + x2 = 0 + -588 Combine like terms: 0 + -588 = -588 -59x + x2 = -588 The x term is -59x. Take half its coefficient (-29.5). Square it (870.25) and add it to both sides. Add '870.25' to each side of the equation. -59x + 870.25 + x2 = -588 + 870.25 Reorder the terms: 870.25 + -59x + x2 = -588 + 870.25 Combine like terms: -588 + 870.25 = 282.25 870.25 + -59x + x2 = 282.25 Factor a perfect square on the left side: (x + -29.5)(x + -29.5) = 282.25 Calculate the square root of the right side: 16.800297616 Break this problem into two subproblems by setting (x + -29.5) equal to 16.800297616 and -16.800297616.Subproblem 1
x + -29.5 = 16.800297616 Simplifying x + -29.5 = 16.800297616 Reorder the terms: -29.5 + x = 16.800297616 Solving -29.5 + x = 16.800297616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.5' to each side of the equation. -29.5 + 29.5 + x = 16.800297616 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x = 16.800297616 + 29.5 x = 16.800297616 + 29.5 Combine like terms: 16.800297616 + 29.5 = 46.300297616 x = 46.300297616 Simplifying x = 46.300297616Subproblem 2
x + -29.5 = -16.800297616 Simplifying x + -29.5 = -16.800297616 Reorder the terms: -29.5 + x = -16.800297616 Solving -29.5 + x = -16.800297616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.5' to each side of the equation. -29.5 + 29.5 + x = -16.800297616 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x = -16.800297616 + 29.5 x = -16.800297616 + 29.5 Combine like terms: -16.800297616 + 29.5 = 12.699702384 x = 12.699702384 Simplifying x = 12.699702384Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.300297616, 12.699702384}
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