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Simplifying 15x2 + -115x + 10 = 0 Reorder the terms: 10 + -115x + 15x2 = 0 Solving 10 + -115x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -23x + 3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -23x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + -23x + 3x2 = 0 Solving 2 + -23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -7.666666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -7.666666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -7.666666667x + x2 = 0 + -0.6666666667 -7.666666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -7.666666667x + x2 = -0.6666666667 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = -0.6666666667 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = -0.6666666667 + 14.69444445 Combine like terms: -0.6666666667 + 14.69444445 = 14.0277777833 14.69444445 + -7.666666667x + x2 = 14.0277777833 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 14.0277777833 Calculate the square root of the right side: 3.74536751 Break this problem into two subproblems by setting (x + -3.833333334) equal to 3.74536751 and -3.74536751.Subproblem 1
x + -3.833333334 = 3.74536751 Simplifying x + -3.833333334 = 3.74536751 Reorder the terms: -3.833333334 + x = 3.74536751 Solving -3.833333334 + x = 3.74536751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 3.74536751 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 3.74536751 + 3.833333334 x = 3.74536751 + 3.833333334 Combine like terms: 3.74536751 + 3.833333334 = 7.578700844 x = 7.578700844 Simplifying x = 7.578700844Subproblem 2
x + -3.833333334 = -3.74536751 Simplifying x + -3.833333334 = -3.74536751 Reorder the terms: -3.833333334 + x = -3.74536751 Solving -3.833333334 + x = -3.74536751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -3.74536751 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -3.74536751 + 3.833333334 x = -3.74536751 + 3.833333334 Combine like terms: -3.74536751 + 3.833333334 = 0.087965824 x = 0.087965824 Simplifying x = 0.087965824Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.578700844, 0.087965824}Solution
x = {7.578700844, 0.087965824}
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