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Simplifying -2x2 + 12x + 9 = -1(x + 5) Reorder the terms: 9 + 12x + -2x2 = -1(x + 5) Reorder the terms: 9 + 12x + -2x2 = -1(5 + x) 9 + 12x + -2x2 = (5 * -1 + x * -1) 9 + 12x + -2x2 = (-5 + -1x) Solving 9 + 12x + -2x2 = -5 + -1x Solving for variable 'x'. Reorder the terms: 9 + 5 + 12x + x + -2x2 = -5 + -1x + 5 + x Combine like terms: 9 + 5 = 14 14 + 12x + x + -2x2 = -5 + -1x + 5 + x Combine like terms: 12x + x = 13x 14 + 13x + -2x2 = -5 + -1x + 5 + x Reorder the terms: 14 + 13x + -2x2 = -5 + 5 + -1x + x Combine like terms: -5 + 5 = 0 14 + 13x + -2x2 = 0 + -1x + x 14 + 13x + -2x2 = -1x + x Combine like terms: -1x + x = 0 14 + 13x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7 + -6.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -6.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -6.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6.5x + x2 = 0 + 7 -6.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -6.5x + x2 = 7 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 = 7 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 7 + 10.5625 Combine like terms: 7 + 10.5625 = 17.5625 10.5625 + -6.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + -3.25) equal to 4.190763654 and -4.190763654.Subproblem 1
x + -3.25 = 4.190763654 Simplifying x + -3.25 = 4.190763654 Reorder the terms: -3.25 + x = 4.190763654 Solving -3.25 + x = 4.190763654 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 = 4.190763654 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.190763654 + 3.25 x = 4.190763654 + 3.25 Combine like terms: 4.190763654 + 3.25 = 7.440763654 x = 7.440763654 Simplifying x = 7.440763654Subproblem 2
x + -3.25 = -4.190763654 Simplifying x + -3.25 = -4.190763654 Reorder the terms: -3.25 + x = -4.190763654 Solving -3.25 + x = -4.190763654 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 = -4.190763654 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.190763654 + 3.25 x = -4.190763654 + 3.25 Combine like terms: -4.190763654 + 3.25 = -0.940763654 x = -0.940763654 Simplifying x = -0.940763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.440763654, -0.940763654}
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