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Simplifying 60 + -14x2 = x Solving 60 + -14x2 = x Solving for variable 'x'. Reorder the terms: 60 + -1x + -14x2 = x + -1x Combine like terms: x + -1x = 0 60 + -1x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -4.285714286 + 0.07142857143x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + 0.07142857143x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + 0.07142857143x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + 0.07142857143x + x2 = 0 + 4.285714286 0.07142857143x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 0.07142857143x + x2 = 4.285714286 The x term is 0.07142857143x. Take half its coefficient (0.03571428572). Square it (0.001275510204) and add it to both sides. Add '0.001275510204' to each side of the equation. 0.07142857143x + 0.001275510204 + x2 = 4.285714286 + 0.001275510204 Reorder the terms: 0.001275510204 + 0.07142857143x + x2 = 4.285714286 + 0.001275510204 Combine like terms: 4.285714286 + 0.001275510204 = 4.286989796204 0.001275510204 + 0.07142857143x + x2 = 4.286989796204 Factor a perfect square on the left side: (x + 0.03571428572)(x + 0.03571428572) = 4.286989796204 Calculate the square root of the right side: 2.07050472 Break this problem into two subproblems by setting (x + 0.03571428572) equal to 2.07050472 and -2.07050472.Subproblem 1
x + 0.03571428572 = 2.07050472 Simplifying x + 0.03571428572 = 2.07050472 Reorder the terms: 0.03571428572 + x = 2.07050472 Solving 0.03571428572 + x = 2.07050472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = 2.07050472 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = 2.07050472 + -0.03571428572 x = 2.07050472 + -0.03571428572 Combine like terms: 2.07050472 + -0.03571428572 = 2.03479043428 x = 2.03479043428 Simplifying x = 2.03479043428Subproblem 2
x + 0.03571428572 = -2.07050472 Simplifying x + 0.03571428572 = -2.07050472 Reorder the terms: 0.03571428572 + x = -2.07050472 Solving 0.03571428572 + x = -2.07050472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = -2.07050472 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = -2.07050472 + -0.03571428572 x = -2.07050472 + -0.03571428572 Combine like terms: -2.07050472 + -0.03571428572 = -2.10621900572 x = -2.10621900572 Simplifying x = -2.10621900572Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.03479043428, -2.10621900572}
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