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Simplifying 8x2 + -16x + -60 = 7 Reorder the terms: -60 + -16x + 8x2 = 7 Solving -60 + -16x + 8x2 = 7 Solving for variable 'x'. Reorder the terms: -60 + -7 + -16x + 8x2 = 7 + -7 Combine like terms: -60 + -7 = -67 -67 + -16x + 8x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -67 + -16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -8.375 + -2x + x2 = 0 Move the constant term to the right: Add '8.375' to each side of the equation. -8.375 + -2x + 8.375 + x2 = 0 + 8.375 Reorder the terms: -8.375 + 8.375 + -2x + x2 = 0 + 8.375 Combine like terms: -8.375 + 8.375 = 0.000 0.000 + -2x + x2 = 0 + 8.375 -2x + x2 = 0 + 8.375 Combine like terms: 0 + 8.375 = 8.375 -2x + x2 = 8.375 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 = 8.375 + 1 Reorder the terms: 1 + -2x + x2 = 8.375 + 1 Combine like terms: 8.375 + 1 = 9.375 1 + -2x + x2 = 9.375 Factor a perfect square on the left side: (x + -1)(x + -1) = 9.375 Calculate the square root of the right side: 3.061862178 Break this problem into two subproblems by setting (x + -1) equal to 3.061862178 and -3.061862178.Subproblem 1
x + -1 = 3.061862178 Simplifying x + -1 = 3.061862178 Reorder the terms: -1 + x = 3.061862178 Solving -1 + x = 3.061862178 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 = 3.061862178 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.061862178 + 1 x = 3.061862178 + 1 Combine like terms: 3.061862178 + 1 = 4.061862178 x = 4.061862178 Simplifying x = 4.061862178Subproblem 2
x + -1 = -3.061862178 Simplifying x + -1 = -3.061862178 Reorder the terms: -1 + x = -3.061862178 Solving -1 + x = -3.061862178 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 = -3.061862178 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.061862178 + 1 x = -3.061862178 + 1 Combine like terms: -3.061862178 + 1 = -2.061862178 x = -2.061862178 Simplifying x = -2.061862178Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.061862178, -2.061862178}
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