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Simplifying -16x2 + 520 = 12x Reorder the terms: 520 + -16x2 = 12x Solving 520 + -16x2 = 12x Solving for variable 'x'. Reorder the terms: 520 + -12x + -16x2 = 12x + -12x Combine like terms: 12x + -12x = 0 520 + -12x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(130 + -3x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(130 + -3x + -4x2)' equal to zero and attempt to solve: Simplifying 130 + -3x + -4x2 = 0 Solving 130 + -3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -32.5 + 0.75x + x2 = 0 Move the constant term to the right: Add '32.5' to each side of the equation. -32.5 + 0.75x + 32.5 + x2 = 0 + 32.5 Reorder the terms: -32.5 + 32.5 + 0.75x + x2 = 0 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + 0.75x + x2 = 0 + 32.5 0.75x + x2 = 0 + 32.5 Combine like terms: 0 + 32.5 = 32.5 0.75x + x2 = 32.5 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 32.5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 32.5 + 0.140625 Combine like terms: 32.5 + 0.140625 = 32.640625 0.140625 + 0.75x + x2 = 32.640625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 32.640625 Calculate the square root of the right side: 5.713197441 Break this problem into two subproblems by setting (x + 0.375) equal to 5.713197441 and -5.713197441.Subproblem 1
x + 0.375 = 5.713197441 Simplifying x + 0.375 = 5.713197441 Reorder the terms: 0.375 + x = 5.713197441 Solving 0.375 + x = 5.713197441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 5.713197441 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 5.713197441 + -0.375 x = 5.713197441 + -0.375 Combine like terms: 5.713197441 + -0.375 = 5.338197441 x = 5.338197441 Simplifying x = 5.338197441Subproblem 2
x + 0.375 = -5.713197441 Simplifying x + 0.375 = -5.713197441 Reorder the terms: 0.375 + x = -5.713197441 Solving 0.375 + x = -5.713197441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -5.713197441 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -5.713197441 + -0.375 x = -5.713197441 + -0.375 Combine like terms: -5.713197441 + -0.375 = -6.088197441 x = -6.088197441 Simplifying x = -6.088197441Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.338197441, -6.088197441}Solution
x = {5.338197441, -6.088197441}
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