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Simplifying -16x2 + -22x + 150 = 0 Reorder the terms: 150 + -22x + -16x2 = 0 Solving 150 + -22x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(75 + -11x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + -11x + -8x2)' equal to zero and attempt to solve: Simplifying 75 + -11x + -8x2 = 0 Solving 75 + -11x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -9.375 + 1.375x + x2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 1.375x + 9.375 + x2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 1.375x + x2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 1.375x + x2 = 0 + 9.375 1.375x + x2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 1.375x + x2 = 9.375 The x term is 1.375x. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375x + 0.47265625 + x2 = 9.375 + 0.47265625 Reorder the terms: 0.47265625 + 1.375x + x2 = 9.375 + 0.47265625 Combine like terms: 9.375 + 0.47265625 = 9.84765625 0.47265625 + 1.375x + x2 = 9.84765625 Factor a perfect square on the left side: (x + 0.6875)(x + 0.6875) = 9.84765625 Calculate the square root of the right side: 3.138097553 Break this problem into two subproblems by setting (x + 0.6875) equal to 3.138097553 and -3.138097553.Subproblem 1
x + 0.6875 = 3.138097553 Simplifying x + 0.6875 = 3.138097553 Reorder the terms: 0.6875 + x = 3.138097553 Solving 0.6875 + x = 3.138097553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = 3.138097553 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 3.138097553 + -0.6875 x = 3.138097553 + -0.6875 Combine like terms: 3.138097553 + -0.6875 = 2.450597553 x = 2.450597553 Simplifying x = 2.450597553Subproblem 2
x + 0.6875 = -3.138097553 Simplifying x + 0.6875 = -3.138097553 Reorder the terms: 0.6875 + x = -3.138097553 Solving 0.6875 + x = -3.138097553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = -3.138097553 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -3.138097553 + -0.6875 x = -3.138097553 + -0.6875 Combine like terms: -3.138097553 + -0.6875 = -3.825597553 x = -3.825597553 Simplifying x = -3.825597553Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.450597553, -3.825597553}Solution
x = {2.450597553, -3.825597553}
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