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Simplifying 2x * x + 40x = 150 Multiply x * x 2x2 + 40x = 150 Reorder the terms: 40x + 2x2 = 150 Solving 40x + 2x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 40x + 2x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 40x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + 20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-75 + 20x + x2)' equal to zero and attempt to solve: Simplifying -75 + 20x + x2 = 0 Solving -75 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 20x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 20x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 20x + x2 = 0 + 75 20x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 20x + x2 = 75 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 75 + 100 Reorder the terms: 100 + 20x + x2 = 75 + 100 Combine like terms: 75 + 100 = 175 100 + 20x + x2 = 175 Factor a perfect square on the left side: (x + 10)(x + 10) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x + 10) equal to 13.228756555 and -13.228756555.Subproblem 1
x + 10 = 13.228756555 Simplifying x + 10 = 13.228756555 Reorder the terms: 10 + x = 13.228756555 Solving 10 + x = 13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 13.228756555 + -10 Combine like terms: 10 + -10 = 0 0 + x = 13.228756555 + -10 x = 13.228756555 + -10 Combine like terms: 13.228756555 + -10 = 3.228756555 x = 3.228756555 Simplifying x = 3.228756555Subproblem 2
x + 10 = -13.228756555 Simplifying x + 10 = -13.228756555 Reorder the terms: 10 + x = -13.228756555 Solving 10 + x = -13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -13.228756555 + -10 Combine like terms: 10 + -10 = 0 0 + x = -13.228756555 + -10 x = -13.228756555 + -10 Combine like terms: -13.228756555 + -10 = -23.228756555 x = -23.228756555 Simplifying x = -23.228756555Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.228756555, -23.228756555}Solution
x = {3.228756555, -23.228756555}
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