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Simplifying 0 = -16x2 + -112x + -150 Reorder the terms: 0 = -150 + -112x + -16x2 Solving 0 = -150 + -112x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 150 = 150 150 + 112x + 16x2 = -150 + -112x + -16x2 + 150 + 112x + 16x2 Reorder the terms: 150 + 112x + 16x2 = -150 + 150 + -112x + 112x + -16x2 + 16x2 Combine like terms: -150 + 150 = 0 150 + 112x + 16x2 = 0 + -112x + 112x + -16x2 + 16x2 150 + 112x + 16x2 = -112x + 112x + -16x2 + 16x2 Combine like terms: -112x + 112x = 0 150 + 112x + 16x2 = 0 + -16x2 + 16x2 150 + 112x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 150 + 112x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(75 + 56x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + 56x + 8x2)' equal to zero and attempt to solve: Simplifying 75 + 56x + 8x2 = 0 Solving 75 + 56x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 9.375 + 7x + x2 = 0 Move the constant term to the right: Add '-9.375' to each side of the equation. 9.375 + 7x + -9.375 + x2 = 0 + -9.375 Reorder the terms: 9.375 + -9.375 + 7x + x2 = 0 + -9.375 Combine like terms: 9.375 + -9.375 = 0.000 0.000 + 7x + x2 = 0 + -9.375 7x + x2 = 0 + -9.375 Combine like terms: 0 + -9.375 = -9.375 7x + x2 = -9.375 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -9.375 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -9.375 + 12.25 Combine like terms: -9.375 + 12.25 = 2.875 12.25 + 7x + x2 = 2.875 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (x + 3.5) equal to 1.695582496 and -1.695582496.Subproblem 1
x + 3.5 = 1.695582496 Simplifying x + 3.5 = 1.695582496 Reorder the terms: 3.5 + x = 1.695582496 Solving 3.5 + x = 1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 1.695582496 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 1.695582496 + -3.5 x = 1.695582496 + -3.5 Combine like terms: 1.695582496 + -3.5 = -1.804417504 x = -1.804417504 Simplifying x = -1.804417504Subproblem 2
x + 3.5 = -1.695582496 Simplifying x + 3.5 = -1.695582496 Reorder the terms: 3.5 + x = -1.695582496 Solving 3.5 + x = -1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -1.695582496 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -1.695582496 + -3.5 x = -1.695582496 + -3.5 Combine like terms: -1.695582496 + -3.5 = -5.195582496 x = -5.195582496 Simplifying x = -5.195582496Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.804417504, -5.195582496}Solution
x = {-1.804417504, -5.195582496}
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