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Simplifying [4x + -1][4x + -1] = 1499 Reorder the terms: [-1 + 4x][4x + -1] = 1499 Reorder the terms: [-1 + 4x][-1 + 4x] = 1499 Multiply [-1 + 4x] * [-1 + 4x] [-1[-1 + 4x] + 4x * [-1 + 4x]] = 1499 [[-1 * -1 + 4x * -1] + 4x * [-1 + 4x]] = 1499 [[1 + -4x] + 4x * [-1 + 4x]] = 1499 [1 + -4x + [-1 * 4x + 4x * 4x]] = 1499 [1 + -4x + [-4x + 16x2]] = 1499 Combine like terms: -4x + -4x = -8x [1 + -8x + 16x2] = 1499 Solving 1 + -8x + 16x2 = 1499 Solving for variable 'x'. Reorder the terms: 1 + -1499 + -8x + 16x2 = 1499 + -1499 Combine like terms: 1 + -1499 = -1498 -1498 + -8x + 16x2 = 1499 + -1499 Combine like terms: 1499 + -1499 = 0 -1498 + -8x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-749 + -4x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-749 + -4x + 8x2)' equal to zero and attempt to solve: Simplifying -749 + -4x + 8x2 = 0 Solving -749 + -4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -93.625 + -0.5x + x2 = 0 Move the constant term to the right: Add '93.625' to each side of the equation. -93.625 + -0.5x + 93.625 + x2 = 0 + 93.625 Reorder the terms: -93.625 + 93.625 + -0.5x + x2 = 0 + 93.625 Combine like terms: -93.625 + 93.625 = 0.000 0.000 + -0.5x + x2 = 0 + 93.625 -0.5x + x2 = 0 + 93.625 Combine like terms: 0 + 93.625 = 93.625 -0.5x + x2 = 93.625 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 93.625 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 93.625 + 0.0625 Combine like terms: 93.625 + 0.0625 = 93.6875 0.0625 + -0.5x + x2 = 93.6875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 93.6875 Calculate the square root of the right side: 9.679230341 Break this problem into two subproblems by setting (x + -0.25) equal to 9.679230341 and -9.679230341.Subproblem 1
x + -0.25 = 9.679230341 Simplifying x + -0.25 = 9.679230341 Reorder the terms: -0.25 + x = 9.679230341 Solving -0.25 + x = 9.679230341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 9.679230341 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 9.679230341 + 0.25 x = 9.679230341 + 0.25 Combine like terms: 9.679230341 + 0.25 = 9.929230341 x = 9.929230341 Simplifying x = 9.929230341Subproblem 2
x + -0.25 = -9.679230341 Simplifying x + -0.25 = -9.679230341 Reorder the terms: -0.25 + x = -9.679230341 Solving -0.25 + x = -9.679230341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -9.679230341 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -9.679230341 + 0.25 x = -9.679230341 + 0.25 Combine like terms: -9.679230341 + 0.25 = -9.429230341 x = -9.429230341 Simplifying x = -9.429230341Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.929230341, -9.429230341}Solution
x = {9.929230341, -9.429230341}
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