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Simplifying 0 = 8x2 + -15x + -5 + 10x Reorder the terms: 0 = -5 + -15x + 10x + 8x2 Combine like terms: -15x + 10x = -5x 0 = -5 + -5x + 8x2 Solving 0 = -5 + -5x + 8x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + 5x + -8x2 = -5 + -5x + 8x2 + 5 + 5x + -8x2 Reorder the terms: 5 + 5x + -8x2 = -5 + 5 + -5x + 5x + 8x2 + -8x2 Combine like terms: -5 + 5 = 0 5 + 5x + -8x2 = 0 + -5x + 5x + 8x2 + -8x2 5 + 5x + -8x2 = -5x + 5x + 8x2 + -8x2 Combine like terms: -5x + 5x = 0 5 + 5x + -8x2 = 0 + 8x2 + -8x2 5 + 5x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 5 + 5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + -0.625x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.625x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.625x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.625x + x2 = 0 + 0.625 -0.625x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.625x + x2 = 0.625 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 = 0.625 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 0.625 + 0.09765625 Combine like terms: 0.625 + 0.09765625 = 0.72265625 0.09765625 + -0.625x + x2 = 0.72265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 0.72265625 Calculate the square root of the right side: 0.850091907 Break this problem into two subproblems by setting (x + -0.3125) equal to 0.850091907 and -0.850091907.Subproblem 1
x + -0.3125 = 0.850091907 Simplifying x + -0.3125 = 0.850091907 Reorder the terms: -0.3125 + x = 0.850091907 Solving -0.3125 + x = 0.850091907 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 = 0.850091907 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 0.850091907 + 0.3125 x = 0.850091907 + 0.3125 Combine like terms: 0.850091907 + 0.3125 = 1.162591907 x = 1.162591907 Simplifying x = 1.162591907Subproblem 2
x + -0.3125 = -0.850091907 Simplifying x + -0.3125 = -0.850091907 Reorder the terms: -0.3125 + x = -0.850091907 Solving -0.3125 + x = -0.850091907 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 = -0.850091907 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -0.850091907 + 0.3125 x = -0.850091907 + 0.3125 Combine like terms: -0.850091907 + 0.3125 = -0.537591907 x = -0.537591907 Simplifying x = -0.537591907Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.162591907, -0.537591907}
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