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Simplifying 4x2 + -10x + -138 = 0 Reorder the terms: -138 + -10x + 4x2 = 0 Solving -138 + -10x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-69 + -5x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-69 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying -69 + -5x + 2x2 = 0 Solving -69 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -34.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '34.5' to each side of the equation. -34.5 + -2.5x + 34.5 + x2 = 0 + 34.5 Reorder the terms: -34.5 + 34.5 + -2.5x + x2 = 0 + 34.5 Combine like terms: -34.5 + 34.5 = 0.0 0.0 + -2.5x + x2 = 0 + 34.5 -2.5x + x2 = 0 + 34.5 Combine like terms: 0 + 34.5 = 34.5 -2.5x + x2 = 34.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 34.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 34.5 + 1.5625 Combine like terms: 34.5 + 1.5625 = 36.0625 1.5625 + -2.5x + x2 = 36.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 36.0625 Calculate the square root of the right side: 6.005206075 Break this problem into two subproblems by setting (x + -1.25) equal to 6.005206075 and -6.005206075.Subproblem 1
x + -1.25 = 6.005206075 Simplifying x + -1.25 = 6.005206075 Reorder the terms: -1.25 + x = 6.005206075 Solving -1.25 + x = 6.005206075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 6.005206075 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 6.005206075 + 1.25 x = 6.005206075 + 1.25 Combine like terms: 6.005206075 + 1.25 = 7.255206075 x = 7.255206075 Simplifying x = 7.255206075Subproblem 2
x + -1.25 = -6.005206075 Simplifying x + -1.25 = -6.005206075 Reorder the terms: -1.25 + x = -6.005206075 Solving -1.25 + x = -6.005206075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -6.005206075 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -6.005206075 + 1.25 x = -6.005206075 + 1.25 Combine like terms: -6.005206075 + 1.25 = -4.755206075 x = -4.755206075 Simplifying x = -4.755206075Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.255206075, -4.755206075}Solution
x = {7.255206075, -4.755206075}
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