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Simplifying 52x2 + 62x + -15 = 0 Reorder the terms: -15 + 62x + 52x2 = 0 Solving -15 + 62x + 52x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 52 the coefficient of the squared term: Divide each side by '52'. -0.2884615385 + 1.192307692x + x2 = 0 Move the constant term to the right: Add '0.2884615385' to each side of the equation. -0.2884615385 + 1.192307692x + 0.2884615385 + x2 = 0 + 0.2884615385 Reorder the terms: -0.2884615385 + 0.2884615385 + 1.192307692x + x2 = 0 + 0.2884615385 Combine like terms: -0.2884615385 + 0.2884615385 = 0.0000000000 0.0000000000 + 1.192307692x + x2 = 0 + 0.2884615385 1.192307692x + x2 = 0 + 0.2884615385 Combine like terms: 0 + 0.2884615385 = 0.2884615385 1.192307692x + x2 = 0.2884615385 The x term is 1.192307692x. Take half its coefficient (0.596153846). Square it (0.3553994081) and add it to both sides. Add '0.3553994081' to each side of the equation. 1.192307692x + 0.3553994081 + x2 = 0.2884615385 + 0.3553994081 Reorder the terms: 0.3553994081 + 1.192307692x + x2 = 0.2884615385 + 0.3553994081 Combine like terms: 0.2884615385 + 0.3553994081 = 0.6438609466 0.3553994081 + 1.192307692x + x2 = 0.6438609466 Factor a perfect square on the left side: (x + 0.596153846)(x + 0.596153846) = 0.6438609466 Calculate the square root of the right side: 0.802409463 Break this problem into two subproblems by setting (x + 0.596153846) equal to 0.802409463 and -0.802409463.Subproblem 1
x + 0.596153846 = 0.802409463 Simplifying x + 0.596153846 = 0.802409463 Reorder the terms: 0.596153846 + x = 0.802409463 Solving 0.596153846 + x = 0.802409463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.596153846' to each side of the equation. 0.596153846 + -0.596153846 + x = 0.802409463 + -0.596153846 Combine like terms: 0.596153846 + -0.596153846 = 0.000000000 0.000000000 + x = 0.802409463 + -0.596153846 x = 0.802409463 + -0.596153846 Combine like terms: 0.802409463 + -0.596153846 = 0.206255617 x = 0.206255617 Simplifying x = 0.206255617Subproblem 2
x + 0.596153846 = -0.802409463 Simplifying x + 0.596153846 = -0.802409463 Reorder the terms: 0.596153846 + x = -0.802409463 Solving 0.596153846 + x = -0.802409463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.596153846' to each side of the equation. 0.596153846 + -0.596153846 + x = -0.802409463 + -0.596153846 Combine like terms: 0.596153846 + -0.596153846 = 0.000000000 0.000000000 + x = -0.802409463 + -0.596153846 x = -0.802409463 + -0.596153846 Combine like terms: -0.802409463 + -0.596153846 = -1.398563309 x = -1.398563309 Simplifying x = -1.398563309Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.206255617, -1.398563309}
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