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Simplifying 5x2 + -5x = 45 Reorder the terms: -5x + 5x2 = 45 Solving -5x + 5x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -5x + 5x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -5x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + -1x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + -1x + x2)' equal to zero and attempt to solve: Simplifying -9 + -1x + x2 = 0 Solving -9 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -1x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -1x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x + x2 = 0 + 9 -1x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1x + x2 = 9 The x term is -1x. 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 = 9 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + -1x + x2 = 9.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + -0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + -0.5 = 3.041381265 Simplifying x + -0.5 = 3.041381265 Reorder the terms: -0.5 + x = 3.041381265 Solving -0.5 + x = 3.041381265 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 = 3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.041381265 + 0.5 x = 3.041381265 + 0.5 Combine like terms: 3.041381265 + 0.5 = 3.541381265 x = 3.541381265 Simplifying x = 3.541381265Subproblem 2
x + -0.5 = -3.041381265 Simplifying x + -0.5 = -3.041381265 Reorder the terms: -0.5 + x = -3.041381265 Solving -0.5 + x = -3.041381265 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 = -3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.041381265 + 0.5 x = -3.041381265 + 0.5 Combine like terms: -3.041381265 + 0.5 = -2.541381265 x = -2.541381265 Simplifying x = -2.541381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.541381265, -2.541381265}Solution
x = {3.541381265, -2.541381265}
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