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Simplifying 4x2 + -60x + -135 = 0 Reorder the terms: -135 + -60x + 4x2 = 0 Solving -135 + -60x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -33.75 + -15x + x2 = 0 Move the constant term to the right: Add '33.75' to each side of the equation. -33.75 + -15x + 33.75 + x2 = 0 + 33.75 Reorder the terms: -33.75 + 33.75 + -15x + x2 = 0 + 33.75 Combine like terms: -33.75 + 33.75 = 0.00 0.00 + -15x + x2 = 0 + 33.75 -15x + x2 = 0 + 33.75 Combine like terms: 0 + 33.75 = 33.75 -15x + x2 = 33.75 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 33.75 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 33.75 + 56.25 Combine like terms: 33.75 + 56.25 = 90 56.25 + -15x + x2 = 90 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + -7.5) equal to 9.486832981 and -9.486832981.Subproblem 1
x + -7.5 = 9.486832981 Simplifying x + -7.5 = 9.486832981 Reorder the terms: -7.5 + x = 9.486832981 Solving -7.5 + x = 9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 9.486832981 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 9.486832981 + 7.5 x = 9.486832981 + 7.5 Combine like terms: 9.486832981 + 7.5 = 16.986832981 x = 16.986832981 Simplifying x = 16.986832981Subproblem 2
x + -7.5 = -9.486832981 Simplifying x + -7.5 = -9.486832981 Reorder the terms: -7.5 + x = -9.486832981 Solving -7.5 + x = -9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -9.486832981 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -9.486832981 + 7.5 x = -9.486832981 + 7.5 Combine like terms: -9.486832981 + 7.5 = -1.986832981 x = -1.986832981 Simplifying x = -1.986832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.986832981, -1.986832981}
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