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Simplifying -1x2 + 5x = 1.709 Reorder the terms: 5x + -1x2 = 1.709 Solving 5x + -1x2 = 1.709 Solving for variable 'x'. Reorder the terms: -1.709 + 5x + -1x2 = 1.709 + -1.709 Combine like terms: 1.709 + -1.709 = 0.000 -1.709 + 5x + -1x2 = 0.000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1.709 + -5x + x2 = 0.000 Move the constant term to the right: Add '-1.709' to each side of the equation. 1.709 + -5x + -1.709 + x2 = 0.000 + -1.709 Reorder the terms: 1.709 + -1.709 + -5x + x2 = 0.000 + -1.709 Combine like terms: 1.709 + -1.709 = 0.000 0.000 + -5x + x2 = 0.000 + -1.709 -5x + x2 = 0.000 + -1.709 Combine like terms: 0.000 + -1.709 = -1.709 -5x + x2 = -1.709 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -1.709 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1.709 + 6.25 Combine like terms: -1.709 + 6.25 = 4.541 6.25 + -5x + x2 = 4.541 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.541 Calculate the square root of the right side: 2.130962224 Break this problem into two subproblems by setting (x + -2.5) equal to 2.130962224 and -2.130962224.Subproblem 1
x + -2.5 = 2.130962224 Simplifying x + -2.5 = 2.130962224 Reorder the terms: -2.5 + x = 2.130962224 Solving -2.5 + x = 2.130962224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.130962224 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.130962224 + 2.5 x = 2.130962224 + 2.5 Combine like terms: 2.130962224 + 2.5 = 4.630962224 x = 4.630962224 Simplifying x = 4.630962224Subproblem 2
x + -2.5 = -2.130962224 Simplifying x + -2.5 = -2.130962224 Reorder the terms: -2.5 + x = -2.130962224 Solving -2.5 + x = -2.130962224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.130962224 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.130962224 + 2.5 x = -2.130962224 + 2.5 Combine like terms: -2.130962224 + 2.5 = 0.369037776 x = 0.369037776 Simplifying x = 0.369037776Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.630962224, 0.369037776}
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