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Simplifying 8x2 + 15x + -13 = 0 Reorder the terms: -13 + 15x + 8x2 = 0 Solving -13 + 15x + 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'. -1.625 + 1.875x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 1.875x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 1.875x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 1.875x + x2 = 0 + 1.625 1.875x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 1.875x + x2 = 1.625 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 = 1.625 + 0.87890625 Reorder the terms: 0.87890625 + 1.875x + x2 = 1.625 + 0.87890625 Combine like terms: 1.625 + 0.87890625 = 2.50390625 0.87890625 + 1.875x + x2 = 2.50390625 Factor a perfect square on the left side: (x + 0.9375)(x + 0.9375) = 2.50390625 Calculate the square root of the right side: 1.582373613 Break this problem into two subproblems by setting (x + 0.9375) equal to 1.582373613 and -1.582373613.Subproblem 1
x + 0.9375 = 1.582373613 Simplifying x + 0.9375 = 1.582373613 Reorder the terms: 0.9375 + x = 1.582373613 Solving 0.9375 + x = 1.582373613 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 = 1.582373613 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = 1.582373613 + -0.9375 x = 1.582373613 + -0.9375 Combine like terms: 1.582373613 + -0.9375 = 0.644873613 x = 0.644873613 Simplifying x = 0.644873613Subproblem 2
x + 0.9375 = -1.582373613 Simplifying x + 0.9375 = -1.582373613 Reorder the terms: 0.9375 + x = -1.582373613 Solving 0.9375 + x = -1.582373613 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 = -1.582373613 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = -1.582373613 + -0.9375 x = -1.582373613 + -0.9375 Combine like terms: -1.582373613 + -0.9375 = -2.519873613 x = -2.519873613 Simplifying x = -2.519873613Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.644873613, -2.519873613}
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