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Simplifying 8x2 + -3x = 15 Reorder the terms: -3x + 8x2 = 15 Solving -3x + 8x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -3x + 8x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + -0.375x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -0.375x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -0.375x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -0.375x + x2 = 0 + 1.875 -0.375x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -0.375x + x2 = 1.875 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 1.875 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 1.875 + 0.03515625 Combine like terms: 1.875 + 0.03515625 = 1.91015625 0.03515625 + -0.375x + x2 = 1.91015625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 1.91015625 Calculate the square root of the right side: 1.382084024 Break this problem into two subproblems by setting (x + -0.1875) equal to 1.382084024 and -1.382084024.Subproblem 1
x + -0.1875 = 1.382084024 Simplifying x + -0.1875 = 1.382084024 Reorder the terms: -0.1875 + x = 1.382084024 Solving -0.1875 + x = 1.382084024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 1.382084024 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 1.382084024 + 0.1875 x = 1.382084024 + 0.1875 Combine like terms: 1.382084024 + 0.1875 = 1.569584024 x = 1.569584024 Simplifying x = 1.569584024Subproblem 2
x + -0.1875 = -1.382084024 Simplifying x + -0.1875 = -1.382084024 Reorder the terms: -0.1875 + x = -1.382084024 Solving -0.1875 + x = -1.382084024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -1.382084024 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -1.382084024 + 0.1875 x = -1.382084024 + 0.1875 Combine like terms: -1.382084024 + 0.1875 = -1.194584024 x = -1.194584024 Simplifying x = -1.194584024Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.569584024, -1.194584024}
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