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Simplifying 2x2 + -30x + 225 = 237 Reorder the terms: 225 + -30x + 2x2 = 237 Solving 225 + -30x + 2x2 = 237 Solving for variable 'x'. Reorder the terms: 225 + -237 + -30x + 2x2 = 237 + -237 Combine like terms: 225 + -237 = -12 -12 + -30x + 2x2 = 237 + -237 Combine like terms: 237 + -237 = 0 -12 + -30x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -15x + x2)' equal to zero and attempt to solve: Simplifying -6 + -15x + x2 = 0 Solving -6 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -15x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -15x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -15x + x2 = 0 + 6 -15x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -15x + x2 = 6 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 = 6 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 6 + 56.25 Combine like terms: 6 + 56.25 = 62.25 56.25 + -15x + x2 = 62.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + -7.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + -7.5 = 7.889866919 Simplifying x + -7.5 = 7.889866919 Reorder the terms: -7.5 + x = 7.889866919 Solving -7.5 + x = 7.889866919 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 = 7.889866919 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.889866919 + 7.5 x = 7.889866919 + 7.5 Combine like terms: 7.889866919 + 7.5 = 15.389866919 x = 15.389866919 Simplifying x = 15.389866919Subproblem 2
x + -7.5 = -7.889866919 Simplifying x + -7.5 = -7.889866919 Reorder the terms: -7.5 + x = -7.889866919 Solving -7.5 + x = -7.889866919 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 = -7.889866919 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.889866919 + 7.5 x = -7.889866919 + 7.5 Combine like terms: -7.889866919 + 7.5 = -0.389866919 x = -0.389866919 Simplifying x = -0.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.389866919, -0.389866919}Solution
x = {15.389866919, -0.389866919}
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