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Simplifying 6x2 + 4x + -2 = 52 Reorder the terms: -2 + 4x + 6x2 = 52 Solving -2 + 4x + 6x2 = 52 Solving for variable 'x'. Reorder the terms: -2 + -52 + 4x + 6x2 = 52 + -52 Combine like terms: -2 + -52 = -54 -54 + 4x + 6x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -54 + 4x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 2x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying -27 + 2x + 3x2 = 0 Solving -27 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 0.6666666667x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 0.6666666667x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 0.6666666667x + x2 = 0 + 9 0.6666666667x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 0.6666666667x + x2 = 9 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 9 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 9 + 0.1111111112 Combine like terms: 9 + 0.1111111112 = 9.1111111112 0.1111111112 + 0.6666666667x + x2 = 9.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 9.1111111112 Calculate the square root of the right side: 3.018461713 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 3.018461713 and -3.018461713.Subproblem 1
x + 0.3333333334 = 3.018461713 Simplifying x + 0.3333333334 = 3.018461713 Reorder the terms: 0.3333333334 + x = 3.018461713 Solving 0.3333333334 + x = 3.018461713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 3.018461713 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 3.018461713 + -0.3333333334 x = 3.018461713 + -0.3333333334 Combine like terms: 3.018461713 + -0.3333333334 = 2.6851283796 x = 2.6851283796 Simplifying x = 2.6851283796Subproblem 2
x + 0.3333333334 = -3.018461713 Simplifying x + 0.3333333334 = -3.018461713 Reorder the terms: 0.3333333334 + x = -3.018461713 Solving 0.3333333334 + x = -3.018461713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -3.018461713 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -3.018461713 + -0.3333333334 x = -3.018461713 + -0.3333333334 Combine like terms: -3.018461713 + -0.3333333334 = -3.3517950464 x = -3.3517950464 Simplifying x = -3.3517950464Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6851283796, -3.3517950464}Solution
x = {2.6851283796, -3.3517950464}
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