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Simplifying 5x(x + -26) = 63 Reorder the terms: 5x(-26 + x) = 63 (-26 * 5x + x * 5x) = 63 (-130x + 5x2) = 63 Solving -130x + 5x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + -130x + 5x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + -130x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.6 + -26x + x2 = 0 Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + -26x + 12.6 + x2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + -26x + x2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + -26x + x2 = 0 + 12.6 -26x + x2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 -26x + x2 = 12.6 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = 12.6 + 169 Reorder the terms: 169 + -26x + x2 = 12.6 + 169 Combine like terms: 12.6 + 169 = 181.6 169 + -26x + x2 = 181.6 Factor a perfect square on the left side: (x + -13)(x + -13) = 181.6 Calculate the square root of the right side: 13.475904422 Break this problem into two subproblems by setting (x + -13) equal to 13.475904422 and -13.475904422.Subproblem 1
x + -13 = 13.475904422 Simplifying x + -13 = 13.475904422 Reorder the terms: -13 + x = 13.475904422 Solving -13 + x = 13.475904422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 13.475904422 + 13 Combine like terms: -13 + 13 = 0 0 + x = 13.475904422 + 13 x = 13.475904422 + 13 Combine like terms: 13.475904422 + 13 = 26.475904422 x = 26.475904422 Simplifying x = 26.475904422Subproblem 2
x + -13 = -13.475904422 Simplifying x + -13 = -13.475904422 Reorder the terms: -13 + x = -13.475904422 Solving -13 + x = -13.475904422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -13.475904422 + 13 Combine like terms: -13 + 13 = 0 0 + x = -13.475904422 + 13 x = -13.475904422 + 13 Combine like terms: -13.475904422 + 13 = -0.475904422 x = -0.475904422 Simplifying x = -0.475904422Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.475904422, -0.475904422}
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