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Simplifying -16x2 + 20x + 600 = 0 Reorder the terms: 600 + 20x + -16x2 = 0 Solving 600 + 20x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(150 + 5x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(150 + 5x + -4x2)' equal to zero and attempt to solve: Simplifying 150 + 5x + -4x2 = 0 Solving 150 + 5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -37.5 + -1.25x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + -1.25x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + -1.25x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + -1.25x + x2 = 0 + 37.5 -1.25x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 -1.25x + x2 = 37.5 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 37.5 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 37.5 + 0.390625 Combine like terms: 37.5 + 0.390625 = 37.890625 0.390625 + -1.25x + x2 = 37.890625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 37.890625 Calculate the square root of the right side: 6.155536126 Break this problem into two subproblems by setting (x + -0.625) equal to 6.155536126 and -6.155536126.Subproblem 1
x + -0.625 = 6.155536126 Simplifying x + -0.625 = 6.155536126 Reorder the terms: -0.625 + x = 6.155536126 Solving -0.625 + x = 6.155536126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 6.155536126 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 6.155536126 + 0.625 x = 6.155536126 + 0.625 Combine like terms: 6.155536126 + 0.625 = 6.780536126 x = 6.780536126 Simplifying x = 6.780536126Subproblem 2
x + -0.625 = -6.155536126 Simplifying x + -0.625 = -6.155536126 Reorder the terms: -0.625 + x = -6.155536126 Solving -0.625 + x = -6.155536126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -6.155536126 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -6.155536126 + 0.625 x = -6.155536126 + 0.625 Combine like terms: -6.155536126 + 0.625 = -5.530536126 x = -5.530536126 Simplifying x = -5.530536126Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.780536126, -5.530536126}Solution
x = {6.780536126, -5.530536126}
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