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Simplifying -16x2 + 32x + 150 = 0 Reorder the terms: 150 + 32x + -16x2 = 0 Solving 150 + 32x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(75 + 16x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + 16x + -8x2)' equal to zero and attempt to solve: Simplifying 75 + 16x + -8x2 = 0 Solving 75 + 16x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -9.375 + -2x + x2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + -2x + 9.375 + x2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + -2x + x2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + -2x + x2 = 0 + 9.375 -2x + x2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 -2x + x2 = 9.375 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 9.375 + 1 Reorder the terms: 1 + -2x + x2 = 9.375 + 1 Combine like terms: 9.375 + 1 = 10.375 1 + -2x + x2 = 10.375 Factor a perfect square on the left side: (x + -1)(x + -1) = 10.375 Calculate the square root of the right side: 3.221024682 Break this problem into two subproblems by setting (x + -1) equal to 3.221024682 and -3.221024682.Subproblem 1
x + -1 = 3.221024682 Simplifying x + -1 = 3.221024682 Reorder the terms: -1 + x = 3.221024682 Solving -1 + x = 3.221024682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.221024682 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.221024682 + 1 x = 3.221024682 + 1 Combine like terms: 3.221024682 + 1 = 4.221024682 x = 4.221024682 Simplifying x = 4.221024682Subproblem 2
x + -1 = -3.221024682 Simplifying x + -1 = -3.221024682 Reorder the terms: -1 + x = -3.221024682 Solving -1 + x = -3.221024682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.221024682 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.221024682 + 1 x = -3.221024682 + 1 Combine like terms: -3.221024682 + 1 = -2.221024682 x = -2.221024682 Simplifying x = -2.221024682Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.221024682, -2.221024682}Solution
x = {4.221024682, -2.221024682}
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