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Simplifying 8x2 + 25x + -29 = 0 Reorder the terms: -29 + 25x + 8x2 = 0 Solving -29 + 25x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.625 + 3.125x + x2 = 0 Move the constant term to the right: Add '3.625' to each side of the equation. -3.625 + 3.125x + 3.625 + x2 = 0 + 3.625 Reorder the terms: -3.625 + 3.625 + 3.125x + x2 = 0 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + 3.125x + x2 = 0 + 3.625 3.125x + x2 = 0 + 3.625 Combine like terms: 0 + 3.625 = 3.625 3.125x + x2 = 3.625 The x term is 3.125x. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125x + 2.44140625 + x2 = 3.625 + 2.44140625 Reorder the terms: 2.44140625 + 3.125x + x2 = 3.625 + 2.44140625 Combine like terms: 3.625 + 2.44140625 = 6.06640625 2.44140625 + 3.125x + x2 = 6.06640625 Factor a perfect square on the left side: (x + 1.5625)(x + 1.5625) = 6.06640625 Calculate the square root of the right side: 2.463007562 Break this problem into two subproblems by setting (x + 1.5625) equal to 2.463007562 and -2.463007562.Subproblem 1
x + 1.5625 = 2.463007562 Simplifying x + 1.5625 = 2.463007562 Reorder the terms: 1.5625 + x = 2.463007562 Solving 1.5625 + x = 2.463007562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = 2.463007562 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = 2.463007562 + -1.5625 x = 2.463007562 + -1.5625 Combine like terms: 2.463007562 + -1.5625 = 0.900507562 x = 0.900507562 Simplifying x = 0.900507562Subproblem 2
x + 1.5625 = -2.463007562 Simplifying x + 1.5625 = -2.463007562 Reorder the terms: 1.5625 + x = -2.463007562 Solving 1.5625 + x = -2.463007562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = -2.463007562 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = -2.463007562 + -1.5625 x = -2.463007562 + -1.5625 Combine like terms: -2.463007562 + -1.5625 = -4.025507562 x = -4.025507562 Simplifying x = -4.025507562Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.900507562, -4.025507562}
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