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Simplifying 2x + 40 + 4x * 4x + 6x = 180 Reorder the terms for easier multiplication: 2x + 40 + 4 * 4x * x + 6x = 180 Multiply 4 * 4 2x + 40 + 16x * x + 6x = 180 Multiply x * x 2x + 40 + 16x2 + 6x = 180 Reorder the terms: 40 + 2x + 6x + 16x2 = 180 Combine like terms: 2x + 6x = 8x 40 + 8x + 16x2 = 180 Solving 40 + 8x + 16x2 = 180 Solving for variable 'x'. Reorder the terms: 40 + -180 + 8x + 16x2 = 180 + -180 Combine like terms: 40 + -180 = -140 -140 + 8x + 16x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -140 + 8x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-35 + 2x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-35 + 2x + 4x2)' equal to zero and attempt to solve: Simplifying -35 + 2x + 4x2 = 0 Solving -35 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + 0.5x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 0.5x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 0.5x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 0.5x + x2 = 0 + 8.75 0.5x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 0.5x + x2 = 8.75 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 8.75 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 8.75 + 0.0625 Combine like terms: 8.75 + 0.0625 = 8.8125 0.0625 + 0.5x + x2 = 8.8125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 8.8125 Calculate the square root of the right side: 2.968585522 Break this problem into two subproblems by setting (x + 0.25) equal to 2.968585522 and -2.968585522.Subproblem 1
x + 0.25 = 2.968585522 Simplifying x + 0.25 = 2.968585522 Reorder the terms: 0.25 + x = 2.968585522 Solving 0.25 + x = 2.968585522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.968585522 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.968585522 + -0.25 x = 2.968585522 + -0.25 Combine like terms: 2.968585522 + -0.25 = 2.718585522 x = 2.718585522 Simplifying x = 2.718585522Subproblem 2
x + 0.25 = -2.968585522 Simplifying x + 0.25 = -2.968585522 Reorder the terms: 0.25 + x = -2.968585522 Solving 0.25 + x = -2.968585522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.968585522 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.968585522 + -0.25 x = -2.968585522 + -0.25 Combine like terms: -2.968585522 + -0.25 = -3.218585522 x = -3.218585522 Simplifying x = -3.218585522Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.718585522, -3.218585522}Solution
x = {2.718585522, -3.218585522}
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