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Simplifying 14x2 + -2x + -8 = 13 + -3x Reorder the terms: -8 + -2x + 14x2 = 13 + -3x Solving -8 + -2x + 14x2 = 13 + -3x Solving for variable 'x'. Reorder the terms: -8 + -13 + -2x + 3x + 14x2 = 13 + -3x + -13 + 3x Combine like terms: -8 + -13 = -21 -21 + -2x + 3x + 14x2 = 13 + -3x + -13 + 3x Combine like terms: -2x + 3x = 1x -21 + 1x + 14x2 = 13 + -3x + -13 + 3x Reorder the terms: -21 + 1x + 14x2 = 13 + -13 + -3x + 3x Combine like terms: 13 + -13 = 0 -21 + 1x + 14x2 = 0 + -3x + 3x -21 + 1x + 14x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -21 + 1x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.5 + 0.07142857143x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.07142857143x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.07142857143x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.07142857143x + x2 = 0 + 1.5 0.07142857143x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 0.07142857143x + x2 = 1.5 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 = 1.5 + 0.001275510204 Reorder the terms: 0.001275510204 + 0.07142857143x + x2 = 1.5 + 0.001275510204 Combine like terms: 1.5 + 0.001275510204 = 1.501275510204 0.001275510204 + 0.07142857143x + x2 = 1.501275510204 Factor a perfect square on the left side: (x + 0.03571428572)(x + 0.03571428572) = 1.501275510204 Calculate the square root of the right side: 1.225265486 Break this problem into two subproblems by setting (x + 0.03571428572) equal to 1.225265486 and -1.225265486.Subproblem 1
x + 0.03571428572 = 1.225265486 Simplifying x + 0.03571428572 = 1.225265486 Reorder the terms: 0.03571428572 + x = 1.225265486 Solving 0.03571428572 + x = 1.225265486 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 = 1.225265486 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = 1.225265486 + -0.03571428572 x = 1.225265486 + -0.03571428572 Combine like terms: 1.225265486 + -0.03571428572 = 1.18955120028 x = 1.18955120028 Simplifying x = 1.18955120028Subproblem 2
x + 0.03571428572 = -1.225265486 Simplifying x + 0.03571428572 = -1.225265486 Reorder the terms: 0.03571428572 + x = -1.225265486 Solving 0.03571428572 + x = -1.225265486 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 = -1.225265486 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = -1.225265486 + -0.03571428572 x = -1.225265486 + -0.03571428572 Combine like terms: -1.225265486 + -0.03571428572 = -1.26097977172 x = -1.26097977172 Simplifying x = -1.26097977172Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.18955120028, -1.26097977172}
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