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Simplifying 4x + 4(x + 3) + 4x(2x + 1) = 56 Reorder the terms: 4x + 4(3 + x) + 4x(2x + 1) = 56 4x + (3 * 4 + x * 4) + 4x(2x + 1) = 56 4x + (12 + 4x) + 4x(2x + 1) = 56 Reorder the terms: 4x + 12 + 4x + 4x(1 + 2x) = 56 4x + 12 + 4x + (1 * 4x + 2x * 4x) = 56 4x + 12 + 4x + (4x + 8x2) = 56 Reorder the terms: 12 + 4x + 4x + 4x + 8x2 = 56 Combine like terms: 4x + 4x = 8x 12 + 8x + 4x + 8x2 = 56 Combine like terms: 8x + 4x = 12x 12 + 12x + 8x2 = 56 Solving 12 + 12x + 8x2 = 56 Solving for variable 'x'. Reorder the terms: 12 + -56 + 12x + 8x2 = 56 + -56 Combine like terms: 12 + -56 = -44 -44 + 12x + 8x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -44 + 12x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-11 + 3x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-11 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -11 + 3x + 2x2 = 0 Solving -11 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 1.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 1.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 1.5x + x2 = 0 + 5.5 1.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 1.5x + x2 = 5.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 5.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 5.5 + 0.5625 Combine like terms: 5.5 + 0.5625 = 6.0625 0.5625 + 1.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + 0.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + 0.75 = 2.46221445 Simplifying x + 0.75 = 2.46221445 Reorder the terms: 0.75 + x = 2.46221445 Solving 0.75 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.46221445 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.46221445 + -0.75 x = 2.46221445 + -0.75 Combine like terms: 2.46221445 + -0.75 = 1.71221445 x = 1.71221445 Simplifying x = 1.71221445Subproblem 2
x + 0.75 = -2.46221445 Simplifying x + 0.75 = -2.46221445 Reorder the terms: 0.75 + x = -2.46221445 Solving 0.75 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.46221445 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.46221445 + -0.75 x = -2.46221445 + -0.75 Combine like terms: -2.46221445 + -0.75 = -3.21221445 x = -3.21221445 Simplifying x = -3.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.71221445, -3.21221445}Solution
x = {1.71221445, -3.21221445}
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