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Simplifying 0 = 16x2 + -228x + 364 Reorder the terms: 0 = 364 + -228x + 16x2 Solving 0 = 364 + -228x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -364 = -364 -364 + 228x + -16x2 = 364 + -228x + 16x2 + -364 + 228x + -16x2 Reorder the terms: -364 + 228x + -16x2 = 364 + -364 + -228x + 228x + 16x2 + -16x2 Combine like terms: 364 + -364 = 0 -364 + 228x + -16x2 = 0 + -228x + 228x + 16x2 + -16x2 -364 + 228x + -16x2 = -228x + 228x + 16x2 + -16x2 Combine like terms: -228x + 228x = 0 -364 + 228x + -16x2 = 0 + 16x2 + -16x2 -364 + 228x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -364 + 228x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-91 + 57x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-91 + 57x + -4x2)' equal to zero and attempt to solve: Simplifying -91 + 57x + -4x2 = 0 Solving -91 + 57x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 22.75 + -14.25x + x2 = 0 Move the constant term to the right: Add '-22.75' to each side of the equation. 22.75 + -14.25x + -22.75 + x2 = 0 + -22.75 Reorder the terms: 22.75 + -22.75 + -14.25x + x2 = 0 + -22.75 Combine like terms: 22.75 + -22.75 = 0.00 0.00 + -14.25x + x2 = 0 + -22.75 -14.25x + x2 = 0 + -22.75 Combine like terms: 0 + -22.75 = -22.75 -14.25x + x2 = -22.75 The x term is -14.25x. Take half its coefficient (-7.125). Square it (50.765625) and add it to both sides. Add '50.765625' to each side of the equation. -14.25x + 50.765625 + x2 = -22.75 + 50.765625 Reorder the terms: 50.765625 + -14.25x + x2 = -22.75 + 50.765625 Combine like terms: -22.75 + 50.765625 = 28.015625 50.765625 + -14.25x + x2 = 28.015625 Factor a perfect square on the left side: (x + -7.125)(x + -7.125) = 28.015625 Calculate the square root of the right side: 5.29297884 Break this problem into two subproblems by setting (x + -7.125) equal to 5.29297884 and -5.29297884.Subproblem 1
x + -7.125 = 5.29297884 Simplifying x + -7.125 = 5.29297884 Reorder the terms: -7.125 + x = 5.29297884 Solving -7.125 + x = 5.29297884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.125' to each side of the equation. -7.125 + 7.125 + x = 5.29297884 + 7.125 Combine like terms: -7.125 + 7.125 = 0.000 0.000 + x = 5.29297884 + 7.125 x = 5.29297884 + 7.125 Combine like terms: 5.29297884 + 7.125 = 12.41797884 x = 12.41797884 Simplifying x = 12.41797884Subproblem 2
x + -7.125 = -5.29297884 Simplifying x + -7.125 = -5.29297884 Reorder the terms: -7.125 + x = -5.29297884 Solving -7.125 + x = -5.29297884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.125' to each side of the equation. -7.125 + 7.125 + x = -5.29297884 + 7.125 Combine like terms: -7.125 + 7.125 = 0.000 0.000 + x = -5.29297884 + 7.125 x = -5.29297884 + 7.125 Combine like terms: -5.29297884 + 7.125 = 1.83202116 x = 1.83202116 Simplifying x = 1.83202116Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.41797884, 1.83202116}Solution
x = {12.41797884, 1.83202116}
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