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Simplifying 8x2 + 9x = 13 Reorder the terms: 9x + 8x2 = 13 Solving 9x + 8x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 9x + 8x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + 1.125x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 1.125x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 1.125x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 1.125x + x2 = 0 + 1.625 1.125x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 1.125x + x2 = 1.625 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = 1.625 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 1.625 + 0.31640625 Combine like terms: 1.625 + 0.31640625 = 1.94140625 0.31640625 + 1.125x + x2 = 1.94140625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 1.94140625 Calculate the square root of the right side: 1.393343551 Break this problem into two subproblems by setting (x + 0.5625) equal to 1.393343551 and -1.393343551.Subproblem 1
x + 0.5625 = 1.393343551 Simplifying x + 0.5625 = 1.393343551 Reorder the terms: 0.5625 + x = 1.393343551 Solving 0.5625 + x = 1.393343551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 1.393343551 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 1.393343551 + -0.5625 x = 1.393343551 + -0.5625 Combine like terms: 1.393343551 + -0.5625 = 0.830843551 x = 0.830843551 Simplifying x = 0.830843551Subproblem 2
x + 0.5625 = -1.393343551 Simplifying x + 0.5625 = -1.393343551 Reorder the terms: 0.5625 + x = -1.393343551 Solving 0.5625 + x = -1.393343551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -1.393343551 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -1.393343551 + -0.5625 x = -1.393343551 + -0.5625 Combine like terms: -1.393343551 + -0.5625 = -1.955843551 x = -1.955843551 Simplifying x = -1.955843551Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.830843551, -1.955843551}
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