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Simplifying 4x2 + 4x + -174 = 0 Reorder the terms: -174 + 4x + 4x2 = 0 Solving -174 + 4x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-87 + 2x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-87 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying -87 + 2x + 2x2 = 0 Solving -87 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -43.5 + x + x2 = 0 Move the constant term to the right: Add '43.5' to each side of the equation. -43.5 + x + 43.5 + x2 = 0 + 43.5 Reorder the terms: -43.5 + 43.5 + x + x2 = 0 + 43.5 Combine like terms: -43.5 + 43.5 = 0.0 0.0 + x + x2 = 0 + 43.5 x + x2 = 0 + 43.5 Combine like terms: 0 + 43.5 = 43.5 x + x2 = 43.5 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 = 43.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 43.5 + 0.25 Combine like terms: 43.5 + 0.25 = 43.75 1.25 + x2 = 43.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 43.75 Calculate the square root of the right side: 6.614378278 Break this problem into two subproblems by setting (x + 0.5) equal to 6.614378278 and -6.614378278.Subproblem 1
x + 0.5 = 6.614378278 Simplifying x + 0.5 = 6.614378278 Reorder the terms: 0.5 + x = 6.614378278 Solving 0.5 + x = 6.614378278 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 = 6.614378278 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.614378278 + -0.5 x = 6.614378278 + -0.5 Combine like terms: 6.614378278 + -0.5 = 6.114378278 x = 6.114378278 Simplifying x = 6.114378278Subproblem 2
x + 0.5 = -6.614378278 Simplifying x + 0.5 = -6.614378278 Reorder the terms: 0.5 + x = -6.614378278 Solving 0.5 + x = -6.614378278 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 = -6.614378278 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.614378278 + -0.5 x = -6.614378278 + -0.5 Combine like terms: -6.614378278 + -0.5 = -7.114378278 x = -7.114378278 Simplifying x = -7.114378278Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.114378278, -7.114378278}Solution
x = {6.114378278, -7.114378278}
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