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Simplifying 0 = 8x2 + 15x + -7 Reorder the terms: 0 = -7 + 15x + 8x2 Solving 0 = -7 + 15x + 8x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + -15x + -8x2 = -7 + 15x + 8x2 + 7 + -15x + -8x2 Reorder the terms: 7 + -15x + -8x2 = -7 + 7 + 15x + -15x + 8x2 + -8x2 Combine like terms: -7 + 7 = 0 7 + -15x + -8x2 = 0 + 15x + -15x + 8x2 + -8x2 7 + -15x + -8x2 = 15x + -15x + 8x2 + -8x2 Combine like terms: 15x + -15x = 0 7 + -15x + -8x2 = 0 + 8x2 + -8x2 7 + -15x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 7 + -15x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.875 + 1.875x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 1.875x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 1.875x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 1.875x + x2 = 0 + 0.875 1.875x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 1.875x + x2 = 0.875 The x term is 1.875x. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875x + 0.87890625 + x2 = 0.875 + 0.87890625 Reorder the terms: 0.87890625 + 1.875x + x2 = 0.875 + 0.87890625 Combine like terms: 0.875 + 0.87890625 = 1.75390625 0.87890625 + 1.875x + x2 = 1.75390625 Factor a perfect square on the left side: (x + 0.9375)(x + 0.9375) = 1.75390625 Calculate the square root of the right side: 1.324351256 Break this problem into two subproblems by setting (x + 0.9375) equal to 1.324351256 and -1.324351256.Subproblem 1
x + 0.9375 = 1.324351256 Simplifying x + 0.9375 = 1.324351256 Reorder the terms: 0.9375 + x = 1.324351256 Solving 0.9375 + x = 1.324351256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = 1.324351256 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = 1.324351256 + -0.9375 x = 1.324351256 + -0.9375 Combine like terms: 1.324351256 + -0.9375 = 0.386851256 x = 0.386851256 Simplifying x = 0.386851256Subproblem 2
x + 0.9375 = -1.324351256 Simplifying x + 0.9375 = -1.324351256 Reorder the terms: 0.9375 + x = -1.324351256 Solving 0.9375 + x = -1.324351256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = -1.324351256 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = -1.324351256 + -0.9375 x = -1.324351256 + -0.9375 Combine like terms: -1.324351256 + -0.9375 = -2.261851256 x = -2.261851256 Simplifying x = -2.261851256Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.386851256, -2.261851256}
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