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Simplifying 10x2 + -10x + -138 = 0 Reorder the terms: -138 + -10x + 10x2 = 0 Solving -138 + -10x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-69 + -5x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-69 + -5x + 5x2)' equal to zero and attempt to solve: Simplifying -69 + -5x + 5x2 = 0 Solving -69 + -5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -13.8 + -1x + x2 = 0 Move the constant term to the right: Add '13.8' to each side of the equation. -13.8 + -1x + 13.8 + x2 = 0 + 13.8 Reorder the terms: -13.8 + 13.8 + -1x + x2 = 0 + 13.8 Combine like terms: -13.8 + 13.8 = 0.0 0.0 + -1x + x2 = 0 + 13.8 -1x + x2 = 0 + 13.8 Combine like terms: 0 + 13.8 = 13.8 -1x + x2 = 13.8 The x term is -1x. 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. -1x + 0.25 + x2 = 13.8 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 13.8 + 0.25 Combine like terms: 13.8 + 0.25 = 14.05 0.25 + -1x + x2 = 14.05 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 14.05 Calculate the square root of the right side: 3.748332963 Break this problem into two subproblems by setting (x + -0.5) equal to 3.748332963 and -3.748332963.Subproblem 1
x + -0.5 = 3.748332963 Simplifying x + -0.5 = 3.748332963 Reorder the terms: -0.5 + x = 3.748332963 Solving -0.5 + x = 3.748332963 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 = 3.748332963 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.748332963 + 0.5 x = 3.748332963 + 0.5 Combine like terms: 3.748332963 + 0.5 = 4.248332963 x = 4.248332963 Simplifying x = 4.248332963Subproblem 2
x + -0.5 = -3.748332963 Simplifying x + -0.5 = -3.748332963 Reorder the terms: -0.5 + x = -3.748332963 Solving -0.5 + x = -3.748332963 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 = -3.748332963 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.748332963 + 0.5 x = -3.748332963 + 0.5 Combine like terms: -3.748332963 + 0.5 = -3.248332963 x = -3.248332963 Simplifying x = -3.248332963Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.248332963, -3.248332963}Solution
x = {4.248332963, -3.248332963}
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