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Simplifying 7x + -2x(x + -11) = -23 Reorder the terms: 7x + -2x(-11 + x) = -23 7x + (-11 * -2x + x * -2x) = -23 7x + (22x + -2x2) = -23 Combine like terms: 7x + 22x = 29x 29x + -2x2 = -23 Solving 29x + -2x2 = -23 Solving for variable 'x'. Reorder the terms: 23 + 29x + -2x2 = -23 + 23 Combine like terms: -23 + 23 = 0 23 + 29x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -11.5 + -14.5x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -14.5x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -14.5x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -14.5x + x2 = 0 + 11.5 -14.5x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -14.5x + x2 = 11.5 The x term is -14.5x. Take half its coefficient (-7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. -14.5x + 52.5625 + x2 = 11.5 + 52.5625 Reorder the terms: 52.5625 + -14.5x + x2 = 11.5 + 52.5625 Combine like terms: 11.5 + 52.5625 = 64.0625 52.5625 + -14.5x + x2 = 64.0625 Factor a perfect square on the left side: (x + -7.25)(x + -7.25) = 64.0625 Calculate the square root of the right side: 8.003905297 Break this problem into two subproblems by setting (x + -7.25) equal to 8.003905297 and -8.003905297.Subproblem 1
x + -7.25 = 8.003905297 Simplifying x + -7.25 = 8.003905297 Reorder the terms: -7.25 + x = 8.003905297 Solving -7.25 + x = 8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = 8.003905297 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 8.003905297 + 7.25 x = 8.003905297 + 7.25 Combine like terms: 8.003905297 + 7.25 = 15.253905297 x = 15.253905297 Simplifying x = 15.253905297Subproblem 2
x + -7.25 = -8.003905297 Simplifying x + -7.25 = -8.003905297 Reorder the terms: -7.25 + x = -8.003905297 Solving -7.25 + x = -8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = -8.003905297 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -8.003905297 + 7.25 x = -8.003905297 + 7.25 Combine like terms: -8.003905297 + 7.25 = -0.753905297 x = -0.753905297 Simplifying x = -0.753905297Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.253905297, -0.753905297}
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