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Simplifying 5x2 = 25x + -12.6 Reorder the terms: 5x2 = -12.6 + 25x Solving 5x2 = -12.6 + 25x Solving for variable 'x'. Reorder the terms: 12.6 + -25x + 5x2 = -12.6 + 25x + 12.6 + -25x Reorder the terms: 12.6 + -25x + 5x2 = -12.6 + 12.6 + 25x + -25x Combine like terms: -12.6 + 12.6 = 0.0 12.6 + -25x + 5x2 = 0.0 + 25x + -25x 12.6 + -25x + 5x2 = 25x + -25x Combine like terms: 25x + -25x = 0 12.6 + -25x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.52 + -5x + x2 = 0 Move the constant term to the right: Add '-2.52' to each side of the equation. 2.52 + -5x + -2.52 + x2 = 0 + -2.52 Reorder the terms: 2.52 + -2.52 + -5x + x2 = 0 + -2.52 Combine like terms: 2.52 + -2.52 = 0.00 0.00 + -5x + x2 = 0 + -2.52 -5x + x2 = 0 + -2.52 Combine like terms: 0 + -2.52 = -2.52 -5x + x2 = -2.52 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 = -2.52 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -2.52 + 6.25 Combine like terms: -2.52 + 6.25 = 3.73 6.25 + -5x + x2 = 3.73 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 3.73 Calculate the square root of the right side: 1.931320792 Break this problem into two subproblems by setting (x + -2.5) equal to 1.931320792 and -1.931320792.Subproblem 1
x + -2.5 = 1.931320792 Simplifying x + -2.5 = 1.931320792 Reorder the terms: -2.5 + x = 1.931320792 Solving -2.5 + x = 1.931320792 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 = 1.931320792 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.931320792 + 2.5 x = 1.931320792 + 2.5 Combine like terms: 1.931320792 + 2.5 = 4.431320792 x = 4.431320792 Simplifying x = 4.431320792Subproblem 2
x + -2.5 = -1.931320792 Simplifying x + -2.5 = -1.931320792 Reorder the terms: -2.5 + x = -1.931320792 Solving -2.5 + x = -1.931320792 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 = -1.931320792 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.931320792 + 2.5 x = -1.931320792 + 2.5 Combine like terms: -1.931320792 + 2.5 = 0.568679208 x = 0.568679208 Simplifying x = 0.568679208Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.431320792, 0.568679208}
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