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Simplifying (3x + -2)(x + 5) = (4 + x2) Reorder the terms: (-2 + 3x)(x + 5) = (4 + x2) Reorder the terms: (-2 + 3x)(5 + x) = (4 + x2) Multiply (-2 + 3x) * (5 + x) (-2(5 + x) + 3x * (5 + x)) = (4 + x2) ((5 * -2 + x * -2) + 3x * (5 + x)) = (4 + x2) ((-10 + -2x) + 3x * (5 + x)) = (4 + x2) (-10 + -2x + (5 * 3x + x * 3x)) = (4 + x2) (-10 + -2x + (15x + 3x2)) = (4 + x2) Combine like terms: -2x + 15x = 13x (-10 + 13x + 3x2) = (4 + x2) Remove parenthesis around (4 + x2) -10 + 13x + 3x2 = 4 + x2 Solving -10 + 13x + 3x2 = 4 + x2 Solving for variable 'x'. Reorder the terms: -10 + -4 + 13x + 3x2 + -1x2 = 4 + x2 + -4 + -1x2 Combine like terms: -10 + -4 = -14 -14 + 13x + 3x2 + -1x2 = 4 + x2 + -4 + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -14 + 13x + 2x2 = 4 + x2 + -4 + -1x2 Reorder the terms: -14 + 13x + 2x2 = 4 + -4 + x2 + -1x2 Combine like terms: 4 + -4 = 0 -14 + 13x + 2x2 = 0 + x2 + -1x2 -14 + 13x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 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 = 0.940763654 x = 0.940763654 Simplifying x = 0.940763654Subproblem 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 = -7.440763654 x = -7.440763654 Simplifying x = -7.440763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.940763654, -7.440763654}
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