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Simplifying 8x2 + 8x + -9 = 0 Reorder the terms: -9 + 8x + 8x2 = 0 Solving -9 + 8x + 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'. -1.125 + x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x + x2 = 0 + 1.125 x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 x + x2 = 1.125 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 1.125 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.125 + 0.25 Combine like terms: 1.125 + 0.25 = 1.375 1.25 + x2 = 1.375 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.375 Calculate the square root of the right side: 1.17260394 Break this problem into two subproblems by setting (x + 0.5) equal to 1.17260394 and -1.17260394.Subproblem 1
x + 0.5 = 1.17260394 Simplifying x + 0.5 = 1.17260394 Reorder the terms: 0.5 + x = 1.17260394 Solving 0.5 + x = 1.17260394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.17260394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.17260394 + -0.5 x = 1.17260394 + -0.5 Combine like terms: 1.17260394 + -0.5 = 0.67260394 x = 0.67260394 Simplifying x = 0.67260394Subproblem 2
x + 0.5 = -1.17260394 Simplifying x + 0.5 = -1.17260394 Reorder the terms: 0.5 + x = -1.17260394 Solving 0.5 + x = -1.17260394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.17260394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.17260394 + -0.5 x = -1.17260394 + -0.5 Combine like terms: -1.17260394 + -0.5 = -1.67260394 x = -1.67260394 Simplifying x = -1.67260394Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.67260394, -1.67260394}
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