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Simplifying 4x2 + 4x + -150 = 0 Reorder the terms: -150 + 4x + 4x2 = 0 Solving -150 + 4x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + 2x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-75 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying -75 + 2x + 2x2 = 0 Solving -75 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -37.5 + x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x + x2 = 0 + 37.5 x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 x + x2 = 37.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 37.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 37.5 + 0.25 Combine like terms: 37.5 + 0.25 = 37.75 1.25 + x2 = 37.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 37.75 Calculate the square root of the right side: 6.144102864 Break this problem into two subproblems by setting (x + 0.5) equal to 6.144102864 and -6.144102864.Subproblem 1
x + 0.5 = 6.144102864 Simplifying x + 0.5 = 6.144102864 Reorder the terms: 0.5 + x = 6.144102864 Solving 0.5 + x = 6.144102864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.144102864 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.144102864 + -0.5 x = 6.144102864 + -0.5 Combine like terms: 6.144102864 + -0.5 = 5.644102864 x = 5.644102864 Simplifying x = 5.644102864Subproblem 2
x + 0.5 = -6.144102864 Simplifying x + 0.5 = -6.144102864 Reorder the terms: 0.5 + x = -6.144102864 Solving 0.5 + x = -6.144102864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.144102864 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.144102864 + -0.5 x = -6.144102864 + -0.5 Combine like terms: -6.144102864 + -0.5 = -6.644102864 x = -6.644102864 Simplifying x = -6.644102864Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.644102864, -6.644102864}Solution
x = {5.644102864, -6.644102864}
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