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Simplifying 32 = 2x2 + -7x + 3 Reorder the terms: 32 = 3 + -7x + 2x2 Solving 32 = 3 + -7x + 2x2 Solving for variable 'x'. Combine like terms: 32 + -3 = 29 29 + 7x + -2x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2 Reorder the terms: 29 + 7x + -2x2 = 3 + -3 + -7x + 7x + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 29 + 7x + -2x2 = 0 + -7x + 7x + 2x2 + -2x2 29 + 7x + -2x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 29 + 7x + -2x2 = 0 + 2x2 + -2x2 29 + 7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 29 + 7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -14.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + -3.5x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + -3.5x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + -3.5x + x2 = 0 + 14.5 -3.5x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 -3.5x + x2 = 14.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 14.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 14.5 + 3.0625 Combine like terms: 14.5 + 3.0625 = 17.5625 3.0625 + -3.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + -1.75) equal to 4.190763654 and -4.190763654.Subproblem 1
x + -1.75 = 4.190763654 Simplifying x + -1.75 = 4.190763654 Reorder the terms: -1.75 + x = 4.190763654 Solving -1.75 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 4.190763654 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 4.190763654 + 1.75 x = 4.190763654 + 1.75 Combine like terms: 4.190763654 + 1.75 = 5.940763654 x = 5.940763654 Simplifying x = 5.940763654Subproblem 2
x + -1.75 = -4.190763654 Simplifying x + -1.75 = -4.190763654 Reorder the terms: -1.75 + x = -4.190763654 Solving -1.75 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -4.190763654 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -4.190763654 + 1.75 x = -4.190763654 + 1.75 Combine like terms: -4.190763654 + 1.75 = -2.440763654 x = -2.440763654 Simplifying x = -2.440763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.940763654, -2.440763654}
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