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Simplifying 8x2 + 36x + -13 = 0 Reorder the terms: -13 + 36x + 8x2 = 0 Solving -13 + 36x + 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'. -1.625 + 4.5x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 4.5x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 4.5x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 4.5x + x2 = 0 + 1.625 4.5x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 4.5x + x2 = 1.625 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 1.625 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 1.625 + 5.0625 Combine like terms: 1.625 + 5.0625 = 6.6875 5.0625 + 4.5x + x2 = 6.6875 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 6.6875 Calculate the square root of the right side: 2.586020108 Break this problem into two subproblems by setting (x + 2.25) equal to 2.586020108 and -2.586020108.Subproblem 1
x + 2.25 = 2.586020108 Simplifying x + 2.25 = 2.586020108 Reorder the terms: 2.25 + x = 2.586020108 Solving 2.25 + x = 2.586020108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.586020108 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.586020108 + -2.25 x = 2.586020108 + -2.25 Combine like terms: 2.586020108 + -2.25 = 0.336020108 x = 0.336020108 Simplifying x = 0.336020108Subproblem 2
x + 2.25 = -2.586020108 Simplifying x + 2.25 = -2.586020108 Reorder the terms: 2.25 + x = -2.586020108 Solving 2.25 + x = -2.586020108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.586020108 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.586020108 + -2.25 x = -2.586020108 + -2.25 Combine like terms: -2.586020108 + -2.25 = -4.836020108 x = -4.836020108 Simplifying x = -4.836020108Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.336020108, -4.836020108}
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