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Simplifying 2x(3x + 5) + 6 = 20 Reorder the terms: 2x(5 + 3x) + 6 = 20 (5 * 2x + 3x * 2x) + 6 = 20 (10x + 6x2) + 6 = 20 Reorder the terms: 6 + 10x + 6x2 = 20 Solving 6 + 10x + 6x2 = 20 Solving for variable 'x'. Reorder the terms: 6 + -20 + 10x + 6x2 = 20 + -20 Combine like terms: 6 + -20 = -14 -14 + 10x + 6x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -14 + 10x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying -7 + 5x + 3x2 = 0 Solving -7 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 1.666666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 1.666666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 2.333333333 1.666666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 1.666666667x + x2 = 2.333333333 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 = 2.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 2.333333333 + 0.6944444447 Combine like terms: 2.333333333 + 0.6944444447 = 3.0277777777 0.6944444447 + 1.666666667x + x2 = 3.0277777777 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 3.0277777777 Calculate the square root of the right side: 1.740051085 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.740051085 and -1.740051085.Subproblem 1
x + 0.8333333335 = 1.740051085 Simplifying x + 0.8333333335 = 1.740051085 Reorder the terms: 0.8333333335 + x = 1.740051085 Solving 0.8333333335 + x = 1.740051085 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 = 1.740051085 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.740051085 + -0.8333333335 x = 1.740051085 + -0.8333333335 Combine like terms: 1.740051085 + -0.8333333335 = 0.9067177515 x = 0.9067177515 Simplifying x = 0.9067177515Subproblem 2
x + 0.8333333335 = -1.740051085 Simplifying x + 0.8333333335 = -1.740051085 Reorder the terms: 0.8333333335 + x = -1.740051085 Solving 0.8333333335 + x = -1.740051085 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 = -1.740051085 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.740051085 + -0.8333333335 x = -1.740051085 + -0.8333333335 Combine like terms: -1.740051085 + -0.8333333335 = -2.5733844185 x = -2.5733844185 Simplifying x = -2.5733844185Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9067177515, -2.5733844185}Solution
x = {0.9067177515, -2.5733844185}
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