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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'. Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + 154x + 15x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(25 + 154x + 15x2)' equal to zero and attempt to solve: Simplifying 25 + 154x + 15x2 = 0 Solving 25 + 154x + 15x2 = 0 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 = 24.684444463 26.35111113 + 10.26666667x + x2 = 24.684444463 Factor a perfect square on the left side: (x + 5.133333335)(x + 5.133333335) = 24.684444463 Calculate the square root of the right side: 4.968344238 Break this problem into two subproblems by setting (x + 5.133333335) equal to 4.968344238 and -4.968344238.Subproblem 1
x + 5.133333335 = 4.968344238 Simplifying x + 5.133333335 = 4.968344238 Reorder the terms: 5.133333335 + x = 4.968344238 Solving 5.133333335 + x = 4.968344238 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 = 4.968344238 + -5.133333335 Combine like terms: 5.133333335 + -5.133333335 = 0.000000000 0.000000000 + x = 4.968344238 + -5.133333335 x = 4.968344238 + -5.133333335 Combine like terms: 4.968344238 + -5.133333335 = -0.164989097 x = -0.164989097 Simplifying x = -0.164989097Subproblem 2
x + 5.133333335 = -4.968344238 Simplifying x + 5.133333335 = -4.968344238 Reorder the terms: 5.133333335 + x = -4.968344238 Solving 5.133333335 + x = -4.968344238 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 = -4.968344238 + -5.133333335 Combine like terms: 5.133333335 + -5.133333335 = 0.000000000 0.000000000 + x = -4.968344238 + -5.133333335 x = -4.968344238 + -5.133333335 Combine like terms: -4.968344238 + -5.133333335 = -10.101677573 x = -10.101677573 Simplifying x = -10.101677573Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.164989097, -10.101677573}Solution
x = {-0.164989097, -10.101677573}
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