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Simplifying 30x3 + 57x2 = 18x Reorder the terms: 57x2 + 30x3 = 18x Solving 57x2 + 30x3 = 18x Solving for variable 'x'. Reorder the terms: -18x + 57x2 + 30x3 = 18x + -18x Combine like terms: 18x + -18x = 0 -18x + 57x2 + 30x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-6 + 19x + 10x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-6 + 19x + 10x2)' equal to zero and attempt to solve: Simplifying -6 + 19x + 10x2 = 0 Solving -6 + 19x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.6 + 1.9x + x2 = 0.0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 1.9x + 0.6 + x2 = 0.0 + 0.6 Reorder the terms: -0.6 + 0.6 + 1.9x + x2 = 0.0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 1.9x + x2 = 0.0 + 0.6 1.9x + x2 = 0.0 + 0.6 Combine like terms: 0.0 + 0.6 = 0.6 1.9x + x2 = 0.6 The x term is 1.9x. Take half its coefficient (0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. 1.9x + 0.9025 + x2 = 0.6 + 0.9025 Reorder the terms: 0.9025 + 1.9x + x2 = 0.6 + 0.9025 Combine like terms: 0.6 + 0.9025 = 1.5025 0.9025 + 1.9x + x2 = 1.5025 Factor a perfect square on the left side: (x + 0.95)(x + 0.95) = 1.5025 Calculate the square root of the right side: 1.225765067 Break this problem into two subproblems by setting (x + 0.95) equal to 1.225765067 and -1.225765067.Subproblem 1
x + 0.95 = 1.225765067 Simplifying x + 0.95 = 1.225765067 Reorder the terms: 0.95 + x = 1.225765067 Solving 0.95 + x = 1.225765067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = 1.225765067 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = 1.225765067 + -0.95 x = 1.225765067 + -0.95 Combine like terms: 1.225765067 + -0.95 = 0.275765067 x = 0.275765067 Simplifying x = 0.275765067Subproblem 2
x + 0.95 = -1.225765067 Simplifying x + 0.95 = -1.225765067 Reorder the terms: 0.95 + x = -1.225765067 Solving 0.95 + x = -1.225765067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = -1.225765067 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = -1.225765067 + -0.95 x = -1.225765067 + -0.95 Combine like terms: -1.225765067 + -0.95 = -2.175765067 x = -2.175765067 Simplifying x = -2.175765067Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.275765067, -2.175765067}Solution
x = {0, 0.275765067, -2.175765067}
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