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Simplifying 0 = 2x2 + 120x + 200 Reorder the terms: 0 = 200 + 120x + 2x2 Solving 0 = 200 + 120x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -200 = -200 -200 + -120x + -2x2 = 200 + 120x + 2x2 + -200 + -120x + -2x2 Reorder the terms: -200 + -120x + -2x2 = 200 + -200 + 120x + -120x + 2x2 + -2x2 Combine like terms: 200 + -200 = 0 -200 + -120x + -2x2 = 0 + 120x + -120x + 2x2 + -2x2 -200 + -120x + -2x2 = 120x + -120x + 2x2 + -2x2 Combine like terms: 120x + -120x = 0 -200 + -120x + -2x2 = 0 + 2x2 + -2x2 -200 + -120x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -200 + -120x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(100 + 60x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(100 + 60x + x2)' equal to zero and attempt to solve: Simplifying 100 + 60x + x2 = 0 Solving 100 + 60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + 60x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + 60x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 60x + x2 = 0 + -100 60x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 60x + x2 = -100 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = -100 + 900 Reorder the terms: 900 + 60x + x2 = -100 + 900 Combine like terms: -100 + 900 = 800 900 + 60x + x2 = 800 Factor a perfect square on the left side: (x + 30)(x + 30) = 800 Calculate the square root of the right side: 28.284271247 Break this problem into two subproblems by setting (x + 30) equal to 28.284271247 and -28.284271247.Subproblem 1
x + 30 = 28.284271247 Simplifying x + 30 = 28.284271247 Reorder the terms: 30 + x = 28.284271247 Solving 30 + x = 28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 28.284271247 + -30 Combine like terms: 30 + -30 = 0 0 + x = 28.284271247 + -30 x = 28.284271247 + -30 Combine like terms: 28.284271247 + -30 = -1.715728753 x = -1.715728753 Simplifying x = -1.715728753Subproblem 2
x + 30 = -28.284271247 Simplifying x + 30 = -28.284271247 Reorder the terms: 30 + x = -28.284271247 Solving 30 + x = -28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -28.284271247 + -30 Combine like terms: 30 + -30 = 0 0 + x = -28.284271247 + -30 x = -28.284271247 + -30 Combine like terms: -28.284271247 + -30 = -58.284271247 x = -58.284271247 Simplifying x = -58.284271247Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.715728753, -58.284271247}Solution
x = {-1.715728753, -58.284271247}
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