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Simplifying 3x(3x + -70) = 180 Reorder the terms: 3x(-70 + 3x) = 180 (-70 * 3x + 3x * 3x) = 180 (-210x + 9x2) = 180 Solving -210x + 9x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -210x + 9x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -210x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-60 + -70x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-60 + -70x + 3x2)' equal to zero and attempt to solve: Simplifying -60 + -70x + 3x2 = 0 Solving -60 + -70x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -20 + -23.33333333x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -23.33333333x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -23.33333333x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -23.33333333x + x2 = 0 + 20 -23.33333333x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -23.33333333x + x2 = 20 The x term is -23.33333333x. Take half its coefficient (-11.66666667). Square it (136.1111112) and add it to both sides. Add '136.1111112' to each side of the equation. -23.33333333x + 136.1111112 + x2 = 20 + 136.1111112 Reorder the terms: 136.1111112 + -23.33333333x + x2 = 20 + 136.1111112 Combine like terms: 20 + 136.1111112 = 156.1111112 136.1111112 + -23.33333333x + x2 = 156.1111112 Factor a perfect square on the left side: (x + -11.66666667)(x + -11.66666667) = 156.1111112 Calculate the square root of the right side: 12.494443213 Break this problem into two subproblems by setting (x + -11.66666667) equal to 12.494443213 and -12.494443213.Subproblem 1
x + -11.66666667 = 12.494443213 Simplifying x + -11.66666667 = 12.494443213 Reorder the terms: -11.66666667 + x = 12.494443213 Solving -11.66666667 + x = 12.494443213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.66666667' to each side of the equation. -11.66666667 + 11.66666667 + x = 12.494443213 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + x = 12.494443213 + 11.66666667 x = 12.494443213 + 11.66666667 Combine like terms: 12.494443213 + 11.66666667 = 24.161109883 x = 24.161109883 Simplifying x = 24.161109883Subproblem 2
x + -11.66666667 = -12.494443213 Simplifying x + -11.66666667 = -12.494443213 Reorder the terms: -11.66666667 + x = -12.494443213 Solving -11.66666667 + x = -12.494443213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.66666667' to each side of the equation. -11.66666667 + 11.66666667 + x = -12.494443213 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + x = -12.494443213 + 11.66666667 x = -12.494443213 + 11.66666667 Combine like terms: -12.494443213 + 11.66666667 = -0.827776543 x = -0.827776543 Simplifying x = -0.827776543Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.161109883, -0.827776543}Solution
x = {24.161109883, -0.827776543}
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