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Simplifying 26x2 + 50 = x2 + 70x Reorder the terms: 50 + 26x2 = x2 + 70x Reorder the terms: 50 + 26x2 = 70x + x2 Solving 50 + 26x2 = 70x + x2 Solving for variable 'x'. Reorder the terms: 50 + -70x + 26x2 + -1x2 = 70x + x2 + -70x + -1x2 Combine like terms: 26x2 + -1x2 = 25x2 50 + -70x + 25x2 = 70x + x2 + -70x + -1x2 Reorder the terms: 50 + -70x + 25x2 = 70x + -70x + x2 + -1x2 Combine like terms: 70x + -70x = 0 50 + -70x + 25x2 = 0 + x2 + -1x2 50 + -70x + 25x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 50 + -70x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(10 + -14x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + -14x + 5x2)' equal to zero and attempt to solve: Simplifying 10 + -14x + 5x2 = 0 Solving 10 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + -2.8x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.8x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2.8x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.8x + x2 = 0 + -2 -2.8x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.8x + x2 = -2 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = -2 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = -2 + 1.96 Combine like terms: -2 + 1.96 = -0.04 1.96 + -2.8x + x2 = -0.04 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = -0.04 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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