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Simplifying 4x2 + 22x + -40 = 0 Reorder the terms: -40 + 22x + 4x2 = 0 Solving -40 + 22x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 11x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + 11x + 2x2)' equal to zero and attempt to solve: Simplifying -20 + 11x + 2x2 = 0 Solving -20 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + 5.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 5.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 5.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 5.5x + x2 = 0 + 10 5.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 5.5x + x2 = 10 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 10 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 10 + 7.5625 Combine like terms: 10 + 7.5625 = 17.5625 7.5625 + 5.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + 2.75) equal to 4.190763654 and -4.190763654.Subproblem 1
x + 2.75 = 4.190763654 Simplifying x + 2.75 = 4.190763654 Reorder the terms: 2.75 + x = 4.190763654 Solving 2.75 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 4.190763654 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 4.190763654 + -2.75 x = 4.190763654 + -2.75 Combine like terms: 4.190763654 + -2.75 = 1.440763654 x = 1.440763654 Simplifying x = 1.440763654Subproblem 2
x + 2.75 = -4.190763654 Simplifying x + 2.75 = -4.190763654 Reorder the terms: 2.75 + x = -4.190763654 Solving 2.75 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -4.190763654 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -4.190763654 + -2.75 x = -4.190763654 + -2.75 Combine like terms: -4.190763654 + -2.75 = -6.940763654 x = -6.940763654 Simplifying x = -6.940763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.440763654, -6.940763654}Solution
x = {1.440763654, -6.940763654}
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