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Simplifying 60x2 + 40x + -192 = 0 Reorder the terms: -192 + 40x + 60x2 = 0 Solving -192 + 40x + 60x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-48 + 10x + 15x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-48 + 10x + 15x2)' equal to zero and attempt to solve: Simplifying -48 + 10x + 15x2 = 0 Solving -48 + 10x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -3.2 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 0.6666666667x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 0.6666666667x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 0.6666666667x + x2 = 0 + 3.2 0.6666666667x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 0.6666666667x + x2 = 3.2 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 3.2 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 3.2 + 0.1111111112 Combine like terms: 3.2 + 0.1111111112 = 3.3111111112 0.1111111112 + 0.6666666667x + x2 = 3.3111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 3.3111111112 Calculate the square root of the right side: 1.819645875 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.819645875 and -1.819645875.Subproblem 1
x + 0.3333333334 = 1.819645875 Simplifying x + 0.3333333334 = 1.819645875 Reorder the terms: 0.3333333334 + x = 1.819645875 Solving 0.3333333334 + x = 1.819645875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.819645875 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.819645875 + -0.3333333334 x = 1.819645875 + -0.3333333334 Combine like terms: 1.819645875 + -0.3333333334 = 1.4863125416 x = 1.4863125416 Simplifying x = 1.4863125416Subproblem 2
x + 0.3333333334 = -1.819645875 Simplifying x + 0.3333333334 = -1.819645875 Reorder the terms: 0.3333333334 + x = -1.819645875 Solving 0.3333333334 + x = -1.819645875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.819645875 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.819645875 + -0.3333333334 x = -1.819645875 + -0.3333333334 Combine like terms: -1.819645875 + -0.3333333334 = -2.1529792084 x = -2.1529792084 Simplifying x = -2.1529792084Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4863125416, -2.1529792084}Solution
x = {1.4863125416, -2.1529792084}
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