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Simplifying 3x + 9 = 2x(x + -5) Reorder the terms: 9 + 3x = 2x(x + -5) Reorder the terms: 9 + 3x = 2x(-5 + x) 9 + 3x = (-5 * 2x + x * 2x) 9 + 3x = (-10x + 2x2) Solving 9 + 3x = -10x + 2x2 Solving for variable 'x'. Combine like terms: 3x + 10x = 13x 9 + 13x + -2x2 = -10x + 2x2 + 10x + -2x2 Reorder the terms: 9 + 13x + -2x2 = -10x + 10x + 2x2 + -2x2 Combine like terms: -10x + 10x = 0 9 + 13x + -2x2 = 0 + 2x2 + -2x2 9 + 13x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 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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