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Simplifying 2x2 + 10x = 90 Reorder the terms: 10x + 2x2 = 90 Solving 10x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 10x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + 5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + 5x + x2)' equal to zero and attempt to solve: Simplifying -45 + 5x + x2 = 0 Solving -45 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 5x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 5x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 5x + x2 = 0 + 45 5x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 5x + x2 = 45 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 45 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 45 + 6.25 Combine like terms: 45 + 6.25 = 51.25 6.25 + 5x + x2 = 51.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + 2.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + 2.5 = 7.158910532 Simplifying x + 2.5 = 7.158910532 Reorder the terms: 2.5 + x = 7.158910532 Solving 2.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 7.158910532 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.158910532 + -2.5 x = 7.158910532 + -2.5 Combine like terms: 7.158910532 + -2.5 = 4.658910532 x = 4.658910532 Simplifying x = 4.658910532Subproblem 2
x + 2.5 = -7.158910532 Simplifying x + 2.5 = -7.158910532 Reorder the terms: 2.5 + x = -7.158910532 Solving 2.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -7.158910532 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.158910532 + -2.5 x = -7.158910532 + -2.5 Combine like terms: -7.158910532 + -2.5 = -9.658910532 x = -9.658910532 Simplifying x = -9.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.658910532, -9.658910532}Solution
x = {4.658910532, -9.658910532}
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