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Simplifying 2x2 + 6x = 120 Reorder the terms: 6x + 2x2 = 120 Solving 6x + 2x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 6x + 2x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + 3x + x2)' equal to zero and attempt to solve: Simplifying -60 + 3x + x2 = 0 Solving -60 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 3x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 3x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 3x + x2 = 0 + 60 3x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 3x + x2 = 60 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 60 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 60 + 2.25 Combine like terms: 60 + 2.25 = 62.25 2.25 + 3x + x2 = 62.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + 1.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + 1.5 = 7.889866919 Simplifying x + 1.5 = 7.889866919 Reorder the terms: 1.5 + x = 7.889866919 Solving 1.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.889866919 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.889866919 + -1.5 x = 7.889866919 + -1.5 Combine like terms: 7.889866919 + -1.5 = 6.389866919 x = 6.389866919 Simplifying x = 6.389866919Subproblem 2
x + 1.5 = -7.889866919 Simplifying x + 1.5 = -7.889866919 Reorder the terms: 1.5 + x = -7.889866919 Solving 1.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.889866919 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.889866919 + -1.5 x = -7.889866919 + -1.5 Combine like terms: -7.889866919 + -1.5 = -9.389866919 x = -9.389866919 Simplifying x = -9.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.389866919, -9.389866919}Solution
x = {6.389866919, -9.389866919}
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