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Simplifying 8x2 + -16x + -65 = -10 Reorder the terms: -65 + -16x + 8x2 = -10 Solving -65 + -16x + 8x2 = -10 Solving for variable 'x'. Reorder the terms: -65 + 10 + -16x + 8x2 = -10 + 10 Combine like terms: -65 + 10 = -55 -55 + -16x + 8x2 = -10 + 10 Combine like terms: -10 + 10 = 0 -55 + -16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.875 + -2x + x2 = 0 Move the constant term to the right: Add '6.875' to each side of the equation. -6.875 + -2x + 6.875 + x2 = 0 + 6.875 Reorder the terms: -6.875 + 6.875 + -2x + x2 = 0 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + -2x + x2 = 0 + 6.875 -2x + x2 = 0 + 6.875 Combine like terms: 0 + 6.875 = 6.875 -2x + x2 = 6.875 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 6.875 + 1 Reorder the terms: 1 + -2x + x2 = 6.875 + 1 Combine like terms: 6.875 + 1 = 7.875 1 + -2x + x2 = 7.875 Factor a perfect square on the left side: (x + -1)(x + -1) = 7.875 Calculate the square root of the right side: 2.80624304 Break this problem into two subproblems by setting (x + -1) equal to 2.80624304 and -2.80624304.Subproblem 1
x + -1 = 2.80624304 Simplifying x + -1 = 2.80624304 Reorder the terms: -1 + x = 2.80624304 Solving -1 + x = 2.80624304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.80624304 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.80624304 + 1 x = 2.80624304 + 1 Combine like terms: 2.80624304 + 1 = 3.80624304 x = 3.80624304 Simplifying x = 3.80624304Subproblem 2
x + -1 = -2.80624304 Simplifying x + -1 = -2.80624304 Reorder the terms: -1 + x = -2.80624304 Solving -1 + x = -2.80624304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.80624304 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.80624304 + 1 x = -2.80624304 + 1 Combine like terms: -2.80624304 + 1 = -1.80624304 x = -1.80624304 Simplifying x = -1.80624304Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.80624304, -1.80624304}
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