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Simplifying 2x2 + -28x = 26 Reorder the terms: -28x + 2x2 = 26 Solving -28x + 2x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + -28x + 2x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + -28x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -14x + x2)' equal to zero and attempt to solve: Simplifying -13 + -14x + x2 = 0 Solving -13 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -14x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -14x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -14x + x2 = 0 + 13 -14x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -14x + x2 = 13 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 13 + 49 Reorder the terms: 49 + -14x + x2 = 13 + 49 Combine like terms: 13 + 49 = 62 49 + -14x + x2 = 62 Factor a perfect square on the left side: (x + -7)(x + -7) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x + -7) equal to 7.874007874 and -7.874007874.Subproblem 1
x + -7 = 7.874007874 Simplifying x + -7 = 7.874007874 Reorder the terms: -7 + x = 7.874007874 Solving -7 + x = 7.874007874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.874007874 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.874007874 + 7 x = 7.874007874 + 7 Combine like terms: 7.874007874 + 7 = 14.874007874 x = 14.874007874 Simplifying x = 14.874007874Subproblem 2
x + -7 = -7.874007874 Simplifying x + -7 = -7.874007874 Reorder the terms: -7 + x = -7.874007874 Solving -7 + x = -7.874007874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.874007874 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.874007874 + 7 x = -7.874007874 + 7 Combine like terms: -7.874007874 + 7 = -0.874007874 x = -0.874007874 Simplifying x = -0.874007874Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.874007874, -0.874007874}Solution
x = {14.874007874, -0.874007874}
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