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Simplifying 6x2 + 10x + -6 = 0 Reorder the terms: -6 + 10x + 6x2 = 0 Solving -6 + 10x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying -3 + 5x + 3x2 = 0 Solving -3 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.666666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.666666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.666666667x + x2 = 0 + 1 1.666666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.666666667x + x2 = 1 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 1 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 1 + 0.6944444447 Combine like terms: 1 + 0.6944444447 = 1.6944444447 0.6944444447 + 1.666666667x + x2 = 1.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 1.6944444447 Calculate the square root of the right side: 1.301708279 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.301708279 and -1.301708279.Subproblem 1
x + 0.8333333335 = 1.301708279 Simplifying x + 0.8333333335 = 1.301708279 Reorder the terms: 0.8333333335 + x = 1.301708279 Solving 0.8333333335 + x = 1.301708279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.301708279 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.301708279 + -0.8333333335 x = 1.301708279 + -0.8333333335 Combine like terms: 1.301708279 + -0.8333333335 = 0.4683749455 x = 0.4683749455 Simplifying x = 0.4683749455Subproblem 2
x + 0.8333333335 = -1.301708279 Simplifying x + 0.8333333335 = -1.301708279 Reorder the terms: 0.8333333335 + x = -1.301708279 Solving 0.8333333335 + x = -1.301708279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.301708279 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.301708279 + -0.8333333335 x = -1.301708279 + -0.8333333335 Combine like terms: -1.301708279 + -0.8333333335 = -2.1350416125 x = -2.1350416125 Simplifying x = -2.1350416125Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4683749455, -2.1350416125}Solution
x = {0.4683749455, -2.1350416125}
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