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Simplifying 2x2 + 20x2 + 148x + -192 = 0 Reorder the terms: -192 + 148x + 2x2 + 20x2 = 0 Combine like terms: 2x2 + 20x2 = 22x2 -192 + 148x + 22x2 = 0 Solving -192 + 148x + 22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-96 + 74x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-96 + 74x + 11x2)' equal to zero and attempt to solve: Simplifying -96 + 74x + 11x2 = 0 Solving -96 + 74x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -8.727272727 + 6.727272727x + x2 = 0 Move the constant term to the right: Add '8.727272727' to each side of the equation. -8.727272727 + 6.727272727x + 8.727272727 + x2 = 0 + 8.727272727 Reorder the terms: -8.727272727 + 8.727272727 + 6.727272727x + x2 = 0 + 8.727272727 Combine like terms: -8.727272727 + 8.727272727 = 0.000000000 0.000000000 + 6.727272727x + x2 = 0 + 8.727272727 6.727272727x + x2 = 0 + 8.727272727 Combine like terms: 0 + 8.727272727 = 8.727272727 6.727272727x + x2 = 8.727272727 The x term is 6.727272727x. Take half its coefficient (3.363636364). Square it (11.31404959) and add it to both sides. Add '11.31404959' to each side of the equation. 6.727272727x + 11.31404959 + x2 = 8.727272727 + 11.31404959 Reorder the terms: 11.31404959 + 6.727272727x + x2 = 8.727272727 + 11.31404959 Combine like terms: 8.727272727 + 11.31404959 = 20.041322317 11.31404959 + 6.727272727x + x2 = 20.041322317 Factor a perfect square on the left side: (x + 3.363636364)(x + 3.363636364) = 20.041322317 Calculate the square root of the right side: 4.476753547 Break this problem into two subproblems by setting (x + 3.363636364) equal to 4.476753547 and -4.476753547.Subproblem 1
x + 3.363636364 = 4.476753547 Simplifying x + 3.363636364 = 4.476753547 Reorder the terms: 3.363636364 + x = 4.476753547 Solving 3.363636364 + x = 4.476753547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.363636364' to each side of the equation. 3.363636364 + -3.363636364 + x = 4.476753547 + -3.363636364 Combine like terms: 3.363636364 + -3.363636364 = 0.000000000 0.000000000 + x = 4.476753547 + -3.363636364 x = 4.476753547 + -3.363636364 Combine like terms: 4.476753547 + -3.363636364 = 1.113117183 x = 1.113117183 Simplifying x = 1.113117183Subproblem 2
x + 3.363636364 = -4.476753547 Simplifying x + 3.363636364 = -4.476753547 Reorder the terms: 3.363636364 + x = -4.476753547 Solving 3.363636364 + x = -4.476753547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.363636364' to each side of the equation. 3.363636364 + -3.363636364 + x = -4.476753547 + -3.363636364 Combine like terms: 3.363636364 + -3.363636364 = 0.000000000 0.000000000 + x = -4.476753547 + -3.363636364 x = -4.476753547 + -3.363636364 Combine like terms: -4.476753547 + -3.363636364 = -7.840389911 x = -7.840389911 Simplifying x = -7.840389911Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.113117183, -7.840389911}Solution
x = {1.113117183, -7.840389911}
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