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Simplifying 2x2 + -30x + 29 = 0 Reorder the terms: 29 + -30x + 2x2 = 0 Solving 29 + -30x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14.5 + -15x + x2 = 0 Move the constant term to the right: Add '-14.5' to each side of the equation. 14.5 + -15x + -14.5 + x2 = 0 + -14.5 Reorder the terms: 14.5 + -14.5 + -15x + x2 = 0 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + -15x + x2 = 0 + -14.5 -15x + x2 = 0 + -14.5 Combine like terms: 0 + -14.5 = -14.5 -15x + x2 = -14.5 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -14.5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -14.5 + 56.25 Combine like terms: -14.5 + 56.25 = 41.75 56.25 + -15x + x2 = 41.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 41.75 Calculate the square root of the right side: 6.461423992 Break this problem into two subproblems by setting (x + -7.5) equal to 6.461423992 and -6.461423992.Subproblem 1
x + -7.5 = 6.461423992 Simplifying x + -7.5 = 6.461423992 Reorder the terms: -7.5 + x = 6.461423992 Solving -7.5 + x = 6.461423992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.461423992 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.461423992 + 7.5 x = 6.461423992 + 7.5 Combine like terms: 6.461423992 + 7.5 = 13.961423992 x = 13.961423992 Simplifying x = 13.961423992Subproblem 2
x + -7.5 = -6.461423992 Simplifying x + -7.5 = -6.461423992 Reorder the terms: -7.5 + x = -6.461423992 Solving -7.5 + x = -6.461423992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.461423992 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.461423992 + 7.5 x = -6.461423992 + 7.5 Combine like terms: -6.461423992 + 7.5 = 1.038576008 x = 1.038576008 Simplifying x = 1.038576008Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.961423992, 1.038576008}
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