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Simplifying 19x2 + 11x + -14 = 0 Reorder the terms: -14 + 11x + 19x2 = 0 Solving -14 + 11x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.7368421053 + 0.5789473684x + x2 = 0 Move the constant term to the right: Add '0.7368421053' to each side of the equation. -0.7368421053 + 0.5789473684x + 0.7368421053 + x2 = 0 + 0.7368421053 Reorder the terms: -0.7368421053 + 0.7368421053 + 0.5789473684x + x2 = 0 + 0.7368421053 Combine like terms: -0.7368421053 + 0.7368421053 = 0.0000000000 0.0000000000 + 0.5789473684x + x2 = 0 + 0.7368421053 0.5789473684x + x2 = 0 + 0.7368421053 Combine like terms: 0 + 0.7368421053 = 0.7368421053 0.5789473684x + x2 = 0.7368421053 The x term is 0.5789473684x. Take half its coefficient (0.2894736842). Square it (0.08379501384) and add it to both sides. Add '0.08379501384' to each side of the equation. 0.5789473684x + 0.08379501384 + x2 = 0.7368421053 + 0.08379501384 Reorder the terms: 0.08379501384 + 0.5789473684x + x2 = 0.7368421053 + 0.08379501384 Combine like terms: 0.7368421053 + 0.08379501384 = 0.82063711914 0.08379501384 + 0.5789473684x + x2 = 0.82063711914 Factor a perfect square on the left side: (x + 0.2894736842)(x + 0.2894736842) = 0.82063711914 Calculate the square root of the right side: 0.905890236 Break this problem into two subproblems by setting (x + 0.2894736842) equal to 0.905890236 and -0.905890236.Subproblem 1
x + 0.2894736842 = 0.905890236 Simplifying x + 0.2894736842 = 0.905890236 Reorder the terms: 0.2894736842 + x = 0.905890236 Solving 0.2894736842 + x = 0.905890236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2894736842' to each side of the equation. 0.2894736842 + -0.2894736842 + x = 0.905890236 + -0.2894736842 Combine like terms: 0.2894736842 + -0.2894736842 = 0.0000000000 0.0000000000 + x = 0.905890236 + -0.2894736842 x = 0.905890236 + -0.2894736842 Combine like terms: 0.905890236 + -0.2894736842 = 0.6164165518 x = 0.6164165518 Simplifying x = 0.6164165518Subproblem 2
x + 0.2894736842 = -0.905890236 Simplifying x + 0.2894736842 = -0.905890236 Reorder the terms: 0.2894736842 + x = -0.905890236 Solving 0.2894736842 + x = -0.905890236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2894736842' to each side of the equation. 0.2894736842 + -0.2894736842 + x = -0.905890236 + -0.2894736842 Combine like terms: 0.2894736842 + -0.2894736842 = 0.0000000000 0.0000000000 + x = -0.905890236 + -0.2894736842 x = -0.905890236 + -0.2894736842 Combine like terms: -0.905890236 + -0.2894736842 = -1.1953639202 x = -1.1953639202 Simplifying x = -1.1953639202Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6164165518, -1.1953639202}
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