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Simplifying 540 + -4x * 2 = 4x2 Reorder the terms for easier multiplication: 540 + -4 * 2x = 4x2 Multiply -4 * 2 540 + -8x = 4x2 Solving 540 + -8x = 4x2 Solving for variable 'x'. Combine like terms: 4x2 + -4x2 = 0 540 + -8x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(135 + -2x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(135 + -2x + -1x2)' equal to zero and attempt to solve: Simplifying 135 + -2x + -1x2 = 0 Solving 135 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -135 + 2x + x2 = 0 Move the constant term to the right: Add '135' to each side of the equation. -135 + 2x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + 2x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + 2x + x2 = 0 + 135 2x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 2x + x2 = 135 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 135 + 1 Reorder the terms: 1 + 2x + x2 = 135 + 1 Combine like terms: 135 + 1 = 136 1 + 2x + x2 = 136 Factor a perfect square on the left side: (x + 1)(x + 1) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (x + 1) equal to 11.66190379 and -11.66190379.Subproblem 1
x + 1 = 11.66190379 Simplifying x + 1 = 11.66190379 Reorder the terms: 1 + x = 11.66190379 Solving 1 + x = 11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 11.66190379 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.66190379 + -1 x = 11.66190379 + -1 Combine like terms: 11.66190379 + -1 = 10.66190379 x = 10.66190379 Simplifying x = 10.66190379Subproblem 2
x + 1 = -11.66190379 Simplifying x + 1 = -11.66190379 Reorder the terms: 1 + x = -11.66190379 Solving 1 + x = -11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -11.66190379 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.66190379 + -1 x = -11.66190379 + -1 Combine like terms: -11.66190379 + -1 = -12.66190379 x = -12.66190379 Simplifying x = -12.66190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.66190379, -12.66190379}Solution
x = {10.66190379, -12.66190379}
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