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Simplifying 15x2 + -154x + -25 = 0 Reorder the terms: -25 + -154x + 15x2 = 0 Solving -25 + -154x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.666666667 + -10.26666667x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -10.26666667x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -10.26666667x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -10.26666667x + x2 = 0 + 1.666666667 -10.26666667x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -10.26666667x + x2 = 1.666666667 The x term is -10.26666667x. Take half its coefficient (-5.133333335). Square it (26.35111113) and add it to both sides. Add '26.35111113' to each side of the equation. -10.26666667x + 26.35111113 + x2 = 1.666666667 + 26.35111113 Reorder the terms: 26.35111113 + -10.26666667x + x2 = 1.666666667 + 26.35111113 Combine like terms: 1.666666667 + 26.35111113 = 28.017777797 26.35111113 + -10.26666667x + x2 = 28.017777797 Factor a perfect square on the left side: (x + -5.133333335)(x + -5.133333335) = 28.017777797 Calculate the square root of the right side: 5.293182199 Break this problem into two subproblems by setting (x + -5.133333335) equal to 5.293182199 and -5.293182199.Subproblem 1
x + -5.133333335 = 5.293182199 Simplifying x + -5.133333335 = 5.293182199 Reorder the terms: -5.133333335 + x = 5.293182199 Solving -5.133333335 + x = 5.293182199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.133333335' to each side of the equation. -5.133333335 + 5.133333335 + x = 5.293182199 + 5.133333335 Combine like terms: -5.133333335 + 5.133333335 = 0.000000000 0.000000000 + x = 5.293182199 + 5.133333335 x = 5.293182199 + 5.133333335 Combine like terms: 5.293182199 + 5.133333335 = 10.426515534 x = 10.426515534 Simplifying x = 10.426515534Subproblem 2
x + -5.133333335 = -5.293182199 Simplifying x + -5.133333335 = -5.293182199 Reorder the terms: -5.133333335 + x = -5.293182199 Solving -5.133333335 + x = -5.293182199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.133333335' to each side of the equation. -5.133333335 + 5.133333335 + x = -5.293182199 + 5.133333335 Combine like terms: -5.133333335 + 5.133333335 = 0.000000000 0.000000000 + x = -5.293182199 + 5.133333335 x = -5.293182199 + 5.133333335 Combine like terms: -5.293182199 + 5.133333335 = -0.159848864 x = -0.159848864 Simplifying x = -0.159848864Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.426515534, -0.159848864}
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