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Simplifying 30x2 + -26x + -8 = 0 Reorder the terms: -8 + -26x + 30x2 = 0 Solving -8 + -26x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -13x + 15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -13x + 15x2)' equal to zero and attempt to solve: Simplifying -4 + -13x + 15x2 = 0 Solving -4 + -13x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2666666667 + -0.8666666667x + x2 = 0 Move the constant term to the right: Add '0.2666666667' to each side of the equation. -0.2666666667 + -0.8666666667x + 0.2666666667 + x2 = 0 + 0.2666666667 Reorder the terms: -0.2666666667 + 0.2666666667 + -0.8666666667x + x2 = 0 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + -0.8666666667x + x2 = 0 + 0.2666666667 -0.8666666667x + x2 = 0 + 0.2666666667 Combine like terms: 0 + 0.2666666667 = 0.2666666667 -0.8666666667x + x2 = 0.2666666667 The x term is -0.8666666667x. Take half its coefficient (-0.4333333334). Square it (0.1877777778) and add it to both sides. Add '0.1877777778' to each side of the equation. -0.8666666667x + 0.1877777778 + x2 = 0.2666666667 + 0.1877777778 Reorder the terms: 0.1877777778 + -0.8666666667x + x2 = 0.2666666667 + 0.1877777778 Combine like terms: 0.2666666667 + 0.1877777778 = 0.4544444445 0.1877777778 + -0.8666666667x + x2 = 0.4544444445 Factor a perfect square on the left side: (x + -0.4333333334)(x + -0.4333333334) = 0.4544444445 Calculate the square root of the right side: 0.674124947 Break this problem into two subproblems by setting (x + -0.4333333334) equal to 0.674124947 and -0.674124947.Subproblem 1
x + -0.4333333334 = 0.674124947 Simplifying x + -0.4333333334 = 0.674124947 Reorder the terms: -0.4333333334 + x = 0.674124947 Solving -0.4333333334 + x = 0.674124947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4333333334' to each side of the equation. -0.4333333334 + 0.4333333334 + x = 0.674124947 + 0.4333333334 Combine like terms: -0.4333333334 + 0.4333333334 = 0.0000000000 0.0000000000 + x = 0.674124947 + 0.4333333334 x = 0.674124947 + 0.4333333334 Combine like terms: 0.674124947 + 0.4333333334 = 1.1074582804 x = 1.1074582804 Simplifying x = 1.1074582804Subproblem 2
x + -0.4333333334 = -0.674124947 Simplifying x + -0.4333333334 = -0.674124947 Reorder the terms: -0.4333333334 + x = -0.674124947 Solving -0.4333333334 + x = -0.674124947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4333333334' to each side of the equation. -0.4333333334 + 0.4333333334 + x = -0.674124947 + 0.4333333334 Combine like terms: -0.4333333334 + 0.4333333334 = 0.0000000000 0.0000000000 + x = -0.674124947 + 0.4333333334 x = -0.674124947 + 0.4333333334 Combine like terms: -0.674124947 + 0.4333333334 = -0.2407916136 x = -0.2407916136 Simplifying x = -0.2407916136Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1074582804, -0.2407916136}Solution
x = {1.1074582804, -0.2407916136}
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