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Simplifying 8x2 + 5x + -150 = 0 Reorder the terms: -150 + 5x + 8x2 = 0 Solving -150 + 5x + 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'. -18.75 + 0.625x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + 0.625x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + 0.625x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + 0.625x + x2 = 0 + 18.75 0.625x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 0.625x + x2 = 18.75 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 18.75 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 18.75 + 0.09765625 Combine like terms: 18.75 + 0.09765625 = 18.84765625 0.09765625 + 0.625x + x2 = 18.84765625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 18.84765625 Calculate the square root of the right side: 4.341388747 Break this problem into two subproblems by setting (x + 0.3125) equal to 4.341388747 and -4.341388747.Subproblem 1
x + 0.3125 = 4.341388747 Simplifying x + 0.3125 = 4.341388747 Reorder the terms: 0.3125 + x = 4.341388747 Solving 0.3125 + x = 4.341388747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 4.341388747 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 4.341388747 + -0.3125 x = 4.341388747 + -0.3125 Combine like terms: 4.341388747 + -0.3125 = 4.028888747 x = 4.028888747 Simplifying x = 4.028888747Subproblem 2
x + 0.3125 = -4.341388747 Simplifying x + 0.3125 = -4.341388747 Reorder the terms: 0.3125 + x = -4.341388747 Solving 0.3125 + x = -4.341388747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -4.341388747 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -4.341388747 + -0.3125 x = -4.341388747 + -0.3125 Combine like terms: -4.341388747 + -0.3125 = -4.653888747 x = -4.653888747 Simplifying x = -4.653888747Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.028888747, -4.653888747}
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