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Simplifying x(2x + -13) = 9 Reorder the terms: x(-13 + 2x) = 9 (-13 * x + 2x * x) = 9 (-13x + 2x2) = 9 Solving -13x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -13x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -6.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -6.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -6.5x + x2 = 0 + 4.5 -6.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -6.5x + x2 = 4.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 4.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 4.5 + 10.5625 Combine like terms: 4.5 + 10.5625 = 15.0625 10.5625 + -6.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + -3.25) equal to 3.881043674 and -3.881043674.Subproblem 1
x + -3.25 = 3.881043674 Simplifying x + -3.25 = 3.881043674 Reorder the terms: -3.25 + x = 3.881043674 Solving -3.25 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 3.881043674 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.881043674 + 3.25 x = 3.881043674 + 3.25 Combine like terms: 3.881043674 + 3.25 = 7.131043674 x = 7.131043674 Simplifying x = 7.131043674Subproblem 2
x + -3.25 = -3.881043674 Simplifying x + -3.25 = -3.881043674 Reorder the terms: -3.25 + x = -3.881043674 Solving -3.25 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -3.881043674 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.881043674 + 3.25 x = -3.881043674 + 3.25 Combine like terms: -3.881043674 + 3.25 = -0.631043674 x = -0.631043674 Simplifying x = -0.631043674Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.131043674, -0.631043674}
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