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Simplifying -8x2 + -3x = -6 Reorder the terms: -3x + -8x2 = -6 Solving -3x + -8x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + -3x + -8x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + -3x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.75 + 0.375x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.375x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.375x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.375x + x2 = 0 + 0.75 0.375x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.375x + x2 = 0.75 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 = 0.75 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 0.75 + 0.03515625 Combine like terms: 0.75 + 0.03515625 = 0.78515625 0.03515625 + 0.375x + x2 = 0.78515625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 0.78515625 Calculate the square root of the right side: 0.88609043 Break this problem into two subproblems by setting (x + 0.1875) equal to 0.88609043 and -0.88609043.Subproblem 1
x + 0.1875 = 0.88609043 Simplifying x + 0.1875 = 0.88609043 Reorder the terms: 0.1875 + x = 0.88609043 Solving 0.1875 + x = 0.88609043 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 = 0.88609043 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 0.88609043 + -0.1875 x = 0.88609043 + -0.1875 Combine like terms: 0.88609043 + -0.1875 = 0.69859043 x = 0.69859043 Simplifying x = 0.69859043Subproblem 2
x + 0.1875 = -0.88609043 Simplifying x + 0.1875 = -0.88609043 Reorder the terms: 0.1875 + x = -0.88609043 Solving 0.1875 + x = -0.88609043 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 = -0.88609043 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -0.88609043 + -0.1875 x = -0.88609043 + -0.1875 Combine like terms: -0.88609043 + -0.1875 = -1.07359043 x = -1.07359043 Simplifying x = -1.07359043Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.69859043, -1.07359043}
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