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Simplifying 6x + -4x + -4x * 7x = 26 Reorder the terms for easier multiplication: 6x + -4x + -4 * 7x * x = 26 Multiply -4 * 7 6x + -4x + -28x * x = 26 Multiply x * x 6x + -4x + -28x2 = 26 Combine like terms: 6x + -4x = 2x 2x + -28x2 = 26 Solving 2x + -28x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + 2x + -28x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 2x + -28x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + x + -14x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + x + -14x2)' equal to zero and attempt to solve: Simplifying -13 + x + -14x2 = 0 Solving -13 + x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. 0.9285714286 + -0.07142857143x + x2 = 0 Move the constant term to the right: Add '-0.9285714286' to each side of the equation. 0.9285714286 + -0.07142857143x + -0.9285714286 + x2 = 0 + -0.9285714286 Reorder the terms: 0.9285714286 + -0.9285714286 + -0.07142857143x + x2 = 0 + -0.9285714286 Combine like terms: 0.9285714286 + -0.9285714286 = 0.0000000000 0.0000000000 + -0.07142857143x + x2 = 0 + -0.9285714286 -0.07142857143x + x2 = 0 + -0.9285714286 Combine like terms: 0 + -0.9285714286 = -0.9285714286 -0.07142857143x + x2 = -0.9285714286 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. -0.07142857143x + 0.25 + x2 = -0.9285714286 + 0.25 Reorder the terms: 0.25 + -0.07142857143x + x2 = -0.9285714286 + 0.25 Combine like terms: -0.9285714286 + 0.25 = -0.6785714286 0.25 + -0.07142857143x + x2 = -0.6785714286 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.6785714286 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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