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Simplifying 2x2 + -7x = 136 Reorder the terms: -7x + 2x2 = 136 Solving -7x + 2x2 = 136 Solving for variable 'x'. Reorder the terms: -136 + -7x + 2x2 = 136 + -136 Combine like terms: 136 + -136 = 0 -136 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -68 + -3.5x + x2 = 0 Move the constant term to the right: Add '68' to each side of the equation. -68 + -3.5x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + -3.5x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + -3.5x + x2 = 0 + 68 -3.5x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 -3.5x + x2 = 68 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 68 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 68 + 3.0625 Combine like terms: 68 + 3.0625 = 71.0625 3.0625 + -3.5x + x2 = 71.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 71.0625 Calculate the square root of the right side: 8.42985765 Break this problem into two subproblems by setting (x + -1.75) equal to 8.42985765 and -8.42985765.Subproblem 1
x + -1.75 = 8.42985765 Simplifying x + -1.75 = 8.42985765 Reorder the terms: -1.75 + x = 8.42985765 Solving -1.75 + x = 8.42985765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 8.42985765 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 8.42985765 + 1.75 x = 8.42985765 + 1.75 Combine like terms: 8.42985765 + 1.75 = 10.17985765 x = 10.17985765 Simplifying x = 10.17985765Subproblem 2
x + -1.75 = -8.42985765 Simplifying x + -1.75 = -8.42985765 Reorder the terms: -1.75 + x = -8.42985765 Solving -1.75 + x = -8.42985765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -8.42985765 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -8.42985765 + 1.75 x = -8.42985765 + 1.75 Combine like terms: -8.42985765 + 1.75 = -6.67985765 x = -6.67985765 Simplifying x = -6.67985765Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.17985765, -6.67985765}
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