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Simplifying 2x * 4(3x + 5) = 20 Reorder the terms: 2x * 4(5 + 3x) = 20 Reorder the terms for easier multiplication: 2 * 4x(5 + 3x) = 20 Multiply 2 * 4 8x(5 + 3x) = 20 (5 * 8x + 3x * 8x) = 20 (40x + 24x2) = 20 Solving 40x + 24x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 40x + 24x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 40x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 10x + 6x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 10x + 6x2)' equal to zero and attempt to solve: Simplifying -5 + 10x + 6x2 = 0 Solving -5 + 10x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 1.666666667x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 1.666666667x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 1.666666667x + x2 = 0 + 0.8333333333 1.666666667x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 1.666666667x + x2 = 0.8333333333 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 = 0.8333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 0.8333333333 + 0.6944444447 Combine like terms: 0.8333333333 + 0.6944444447 = 1.527777778 0.6944444447 + 1.666666667x + x2 = 1.527777778 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 1.527777778 Calculate the square root of the right side: 1.236033081 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.236033081 and -1.236033081.Subproblem 1
x + 0.8333333335 = 1.236033081 Simplifying x + 0.8333333335 = 1.236033081 Reorder the terms: 0.8333333335 + x = 1.236033081 Solving 0.8333333335 + x = 1.236033081 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 = 1.236033081 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.236033081 + -0.8333333335 x = 1.236033081 + -0.8333333335 Combine like terms: 1.236033081 + -0.8333333335 = 0.4026997475 x = 0.4026997475 Simplifying x = 0.4026997475Subproblem 2
x + 0.8333333335 = -1.236033081 Simplifying x + 0.8333333335 = -1.236033081 Reorder the terms: 0.8333333335 + x = -1.236033081 Solving 0.8333333335 + x = -1.236033081 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 = -1.236033081 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.236033081 + -0.8333333335 x = -1.236033081 + -0.8333333335 Combine like terms: -1.236033081 + -0.8333333335 = -2.0693664145 x = -2.0693664145 Simplifying x = -2.0693664145Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4026997475, -2.0693664145}Solution
x = {0.4026997475, -2.0693664145}
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