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Simplifying 4x2 + 30x + -150 = 0 Reorder the terms: -150 + 30x + 4x2 = 0 Solving -150 + 30x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + 15x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-75 + 15x + 2x2)' equal to zero and attempt to solve: Simplifying -75 + 15x + 2x2 = 0 Solving -75 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -37.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + 7.5x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + 7.5x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + 7.5x + x2 = 0 + 37.5 7.5x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 7.5x + x2 = 37.5 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 37.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 37.5 + 14.0625 Combine like terms: 37.5 + 14.0625 = 51.5625 14.0625 + 7.5x + x2 = 51.5625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 51.5625 Calculate the square root of the right side: 7.180703308 Break this problem into two subproblems by setting (x + 3.75) equal to 7.180703308 and -7.180703308.Subproblem 1
x + 3.75 = 7.180703308 Simplifying x + 3.75 = 7.180703308 Reorder the terms: 3.75 + x = 7.180703308 Solving 3.75 + x = 7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 7.180703308 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 7.180703308 + -3.75 x = 7.180703308 + -3.75 Combine like terms: 7.180703308 + -3.75 = 3.430703308 x = 3.430703308 Simplifying x = 3.430703308Subproblem 2
x + 3.75 = -7.180703308 Simplifying x + 3.75 = -7.180703308 Reorder the terms: 3.75 + x = -7.180703308 Solving 3.75 + x = -7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -7.180703308 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -7.180703308 + -3.75 x = -7.180703308 + -3.75 Combine like terms: -7.180703308 + -3.75 = -10.930703308 x = -10.930703308 Simplifying x = -10.930703308Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.430703308, -10.930703308}Solution
x = {3.430703308, -10.930703308}
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