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Simplifying 6x2 + 4x + -320 = 0 Reorder the terms: -320 + 4x + 6x2 = 0 Solving -320 + 4x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-160 + 2x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-160 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying -160 + 2x + 3x2 = 0 Solving -160 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -53.33333333 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '53.33333333' to each side of the equation. -53.33333333 + 0.6666666667x + 53.33333333 + x2 = 0 + 53.33333333 Reorder the terms: -53.33333333 + 53.33333333 + 0.6666666667x + x2 = 0 + 53.33333333 Combine like terms: -53.33333333 + 53.33333333 = 0.00000000 0.00000000 + 0.6666666667x + x2 = 0 + 53.33333333 0.6666666667x + x2 = 0 + 53.33333333 Combine like terms: 0 + 53.33333333 = 53.33333333 0.6666666667x + x2 = 53.33333333 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 = 53.33333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 53.33333333 + 0.1111111112 Combine like terms: 53.33333333 + 0.1111111112 = 53.4444444412 0.1111111112 + 0.6666666667x + x2 = 53.4444444412 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 53.4444444412 Calculate the square root of the right side: 7.310570733 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 7.310570733 and -7.310570733.Subproblem 1
x + 0.3333333334 = 7.310570733 Simplifying x + 0.3333333334 = 7.310570733 Reorder the terms: 0.3333333334 + x = 7.310570733 Solving 0.3333333334 + x = 7.310570733 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 = 7.310570733 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 7.310570733 + -0.3333333334 x = 7.310570733 + -0.3333333334 Combine like terms: 7.310570733 + -0.3333333334 = 6.9772373996 x = 6.9772373996 Simplifying x = 6.9772373996Subproblem 2
x + 0.3333333334 = -7.310570733 Simplifying x + 0.3333333334 = -7.310570733 Reorder the terms: 0.3333333334 + x = -7.310570733 Solving 0.3333333334 + x = -7.310570733 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 = -7.310570733 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -7.310570733 + -0.3333333334 x = -7.310570733 + -0.3333333334 Combine like terms: -7.310570733 + -0.3333333334 = -7.6439040664 x = -7.6439040664 Simplifying x = -7.6439040664Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.9772373996, -7.6439040664}Solution
x = {6.9772373996, -7.6439040664}
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