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Simplifying 0 = -16x2 + 150x + 12 Reorder the terms: 0 = 12 + 150x + -16x2 Solving 0 = 12 + 150x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + -150x + 16x2 = 12 + 150x + -16x2 + -12 + -150x + 16x2 Reorder the terms: -12 + -150x + 16x2 = 12 + -12 + 150x + -150x + -16x2 + 16x2 Combine like terms: 12 + -12 = 0 -12 + -150x + 16x2 = 0 + 150x + -150x + -16x2 + 16x2 -12 + -150x + 16x2 = 150x + -150x + -16x2 + 16x2 Combine like terms: 150x + -150x = 0 -12 + -150x + 16x2 = 0 + -16x2 + 16x2 -12 + -150x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -12 + -150x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -75x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -75x + 8x2)' equal to zero and attempt to solve: Simplifying -6 + -75x + 8x2 = 0 Solving -6 + -75x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + -9.375x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -9.375x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -9.375x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -9.375x + x2 = 0 + 0.75 -9.375x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -9.375x + x2 = 0.75 The x term is -9.375x. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375x + 21.97265625 + x2 = 0.75 + 21.97265625 Reorder the terms: 21.97265625 + -9.375x + x2 = 0.75 + 21.97265625 Combine like terms: 0.75 + 21.97265625 = 22.72265625 21.97265625 + -9.375x + x2 = 22.72265625 Factor a perfect square on the left side: (x + -4.6875)(x + -4.6875) = 22.72265625 Calculate the square root of the right side: 4.766828741 Break this problem into two subproblems by setting (x + -4.6875) equal to 4.766828741 and -4.766828741.Subproblem 1
x + -4.6875 = 4.766828741 Simplifying x + -4.6875 = 4.766828741 Reorder the terms: -4.6875 + x = 4.766828741 Solving -4.6875 + x = 4.766828741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + x = 4.766828741 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = 4.766828741 + 4.6875 x = 4.766828741 + 4.6875 Combine like terms: 4.766828741 + 4.6875 = 9.454328741 x = 9.454328741 Simplifying x = 9.454328741Subproblem 2
x + -4.6875 = -4.766828741 Simplifying x + -4.6875 = -4.766828741 Reorder the terms: -4.6875 + x = -4.766828741 Solving -4.6875 + x = -4.766828741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + x = -4.766828741 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = -4.766828741 + 4.6875 x = -4.766828741 + 4.6875 Combine like terms: -4.766828741 + 4.6875 = -0.079328741 x = -0.079328741 Simplifying x = -0.079328741Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.454328741, -0.079328741}Solution
x = {9.454328741, -0.079328741}
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