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Simplifying -6x2 + -25x + -13 = 0 Reorder the terms: -13 + -25x + -6x2 = 0 Solving -13 + -25x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 25x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 25x + 6x2)' equal to zero and attempt to solve: Simplifying 13 + 25x + 6x2 = 0 Solving 13 + 25x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.166666667 + 4.166666667x + x2 = 0 Move the constant term to the right: Add '-2.166666667' to each side of the equation. 2.166666667 + 4.166666667x + -2.166666667 + x2 = 0 + -2.166666667 Reorder the terms: 2.166666667 + -2.166666667 + 4.166666667x + x2 = 0 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + 4.166666667x + x2 = 0 + -2.166666667 4.166666667x + x2 = 0 + -2.166666667 Combine like terms: 0 + -2.166666667 = -2.166666667 4.166666667x + x2 = -2.166666667 The x term is 4.166666667x. Take half its coefficient (2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. 4.166666667x + 4.340277781 + x2 = -2.166666667 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667x + x2 = -2.166666667 + 4.340277781 Combine like terms: -2.166666667 + 4.340277781 = 2.173611114 4.340277781 + 4.166666667x + x2 = 2.173611114 Factor a perfect square on the left side: (x + 2.083333334)(x + 2.083333334) = 2.173611114 Calculate the square root of the right side: 1.474317169 Break this problem into two subproblems by setting (x + 2.083333334) equal to 1.474317169 and -1.474317169.Subproblem 1
x + 2.083333334 = 1.474317169 Simplifying x + 2.083333334 = 1.474317169 Reorder the terms: 2.083333334 + x = 1.474317169 Solving 2.083333334 + x = 1.474317169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = 1.474317169 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = 1.474317169 + -2.083333334 x = 1.474317169 + -2.083333334 Combine like terms: 1.474317169 + -2.083333334 = -0.609016165 x = -0.609016165 Simplifying x = -0.609016165Subproblem 2
x + 2.083333334 = -1.474317169 Simplifying x + 2.083333334 = -1.474317169 Reorder the terms: 2.083333334 + x = -1.474317169 Solving 2.083333334 + x = -1.474317169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = -1.474317169 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = -1.474317169 + -2.083333334 x = -1.474317169 + -2.083333334 Combine like terms: -1.474317169 + -2.083333334 = -3.557650503 x = -3.557650503 Simplifying x = -3.557650503Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.609016165, -3.557650503}Solution
x = {-0.609016165, -3.557650503}
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