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Simplifying 0 = 3x2 + -3x + -135 Reorder the terms: 0 = -135 + -3x + 3x2 Solving 0 = -135 + -3x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 135 = 135 135 + 3x + -3x2 = -135 + -3x + 3x2 + 135 + 3x + -3x2 Reorder the terms: 135 + 3x + -3x2 = -135 + 135 + -3x + 3x + 3x2 + -3x2 Combine like terms: -135 + 135 = 0 135 + 3x + -3x2 = 0 + -3x + 3x + 3x2 + -3x2 135 + 3x + -3x2 = -3x + 3x + 3x2 + -3x2 Combine like terms: -3x + 3x = 0 135 + 3x + -3x2 = 0 + 3x2 + -3x2 135 + 3x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 135 + 3x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(45 + x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(45 + x + -1x2)' equal to zero and attempt to solve: Simplifying 45 + x + -1x2 = 0 Solving 45 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + -1x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -1x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -1x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -1x + x2 = 0 + 45 -1x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -1x + x2 = 45 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 45 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 45 + 0.25 Combine like terms: 45 + 0.25 = 45.25 0.25 + -1x + x2 = 45.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + 0.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + 0.5 = 6.726812024 Simplifying x + 0.5 = 6.726812024 Reorder the terms: 0.5 + x = 6.726812024 Solving 0.5 + x = 6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.726812024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.726812024 + -0.5 x = 6.726812024 + -0.5 Combine like terms: 6.726812024 + -0.5 = 6.226812024 x = 6.226812024 Simplifying x = 6.226812024Subproblem 2
x + 0.5 = -6.726812024 Simplifying x + 0.5 = -6.726812024 Reorder the terms: 0.5 + x = -6.726812024 Solving 0.5 + x = -6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.726812024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.726812024 + -0.5 x = -6.726812024 + -0.5 Combine like terms: -6.726812024 + -0.5 = -7.226812024 x = -7.226812024 Simplifying x = -7.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.226812024, -7.226812024}Solution
x = {6.226812024, -7.226812024}
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