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Simplifying 8x2 + 10x + -15 = 0 Reorder the terms: -15 + 10x + 8x2 = 0 Solving -15 + 10x + 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'. -1.875 + 1.25x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 1.25x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 1.25x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 1.25x + x2 = 0 + 1.875 1.25x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 1.25x + x2 = 1.875 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 1.875 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 1.875 + 0.390625 Combine like terms: 1.875 + 0.390625 = 2.265625 0.390625 + 1.25x + x2 = 2.265625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + 0.625) equal to 1.505199322 and -1.505199322.Subproblem 1
x + 0.625 = 1.505199322 Simplifying x + 0.625 = 1.505199322 Reorder the terms: 0.625 + x = 1.505199322 Solving 0.625 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.505199322 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.505199322 + -0.625 x = 1.505199322 + -0.625 Combine like terms: 1.505199322 + -0.625 = 0.880199322 x = 0.880199322 Simplifying x = 0.880199322Subproblem 2
x + 0.625 = -1.505199322 Simplifying x + 0.625 = -1.505199322 Reorder the terms: 0.625 + x = -1.505199322 Solving 0.625 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.505199322 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.505199322 + -0.625 x = -1.505199322 + -0.625 Combine like terms: -1.505199322 + -0.625 = -2.130199322 x = -2.130199322 Simplifying x = -2.130199322Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.880199322, -2.130199322}
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