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Simplifying -16x2 + -23x + 150 = 0 Reorder the terms: 150 + -23x + -16x2 = 0 Solving 150 + -23x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -9.375 + 1.4375x + x2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 1.4375x + 9.375 + x2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 1.4375x + x2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 1.4375x + x2 = 0 + 9.375 1.4375x + x2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 1.4375x + x2 = 9.375 The x term is 1.4375x. Take half its coefficient (0.71875). Square it (0.5166015625) and add it to both sides. Add '0.5166015625' to each side of the equation. 1.4375x + 0.5166015625 + x2 = 9.375 + 0.5166015625 Reorder the terms: 0.5166015625 + 1.4375x + x2 = 9.375 + 0.5166015625 Combine like terms: 9.375 + 0.5166015625 = 9.8916015625 0.5166015625 + 1.4375x + x2 = 9.8916015625 Factor a perfect square on the left side: (x + 0.71875)(x + 0.71875) = 9.8916015625 Calculate the square root of the right side: 3.145091662 Break this problem into two subproblems by setting (x + 0.71875) equal to 3.145091662 and -3.145091662.Subproblem 1
x + 0.71875 = 3.145091662 Simplifying x + 0.71875 = 3.145091662 Reorder the terms: 0.71875 + x = 3.145091662 Solving 0.71875 + x = 3.145091662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + x = 3.145091662 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + x = 3.145091662 + -0.71875 x = 3.145091662 + -0.71875 Combine like terms: 3.145091662 + -0.71875 = 2.426341662 x = 2.426341662 Simplifying x = 2.426341662Subproblem 2
x + 0.71875 = -3.145091662 Simplifying x + 0.71875 = -3.145091662 Reorder the terms: 0.71875 + x = -3.145091662 Solving 0.71875 + x = -3.145091662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + x = -3.145091662 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + x = -3.145091662 + -0.71875 x = -3.145091662 + -0.71875 Combine like terms: -3.145091662 + -0.71875 = -3.863841662 x = -3.863841662 Simplifying x = -3.863841662Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.426341662, -3.863841662}
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