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Simplifying 6x2 = 4x + 30 Reorder the terms: 6x2 = 30 + 4x Solving 6x2 = 30 + 4x Solving for variable 'x'. Reorder the terms: -30 + -4x + 6x2 = 30 + 4x + -30 + -4x Reorder the terms: -30 + -4x + 6x2 = 30 + -30 + 4x + -4x Combine like terms: 30 + -30 = 0 -30 + -4x + 6x2 = 0 + 4x + -4x -30 + -4x + 6x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -30 + -4x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -2x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying -15 + -2x + 3x2 = 0 Solving -15 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.6666666667x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.6666666667x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.6666666667x + x2 = 0 + 5 -0.6666666667x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.6666666667x + x2 = 5 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 = 5 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 5 + 0.1111111112 Combine like terms: 5 + 0.1111111112 = 5.1111111112 0.1111111112 + -0.6666666667x + x2 = 5.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 5.1111111112 Calculate the square root of the right side: 2.260776661 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 2.260776661 and -2.260776661.Subproblem 1
x + -0.3333333334 = 2.260776661 Simplifying x + -0.3333333334 = 2.260776661 Reorder the terms: -0.3333333334 + x = 2.260776661 Solving -0.3333333334 + x = 2.260776661 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 = 2.260776661 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 2.260776661 + 0.3333333334 x = 2.260776661 + 0.3333333334 Combine like terms: 2.260776661 + 0.3333333334 = 2.5941099944 x = 2.5941099944 Simplifying x = 2.5941099944Subproblem 2
x + -0.3333333334 = -2.260776661 Simplifying x + -0.3333333334 = -2.260776661 Reorder the terms: -0.3333333334 + x = -2.260776661 Solving -0.3333333334 + x = -2.260776661 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 = -2.260776661 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -2.260776661 + 0.3333333334 x = -2.260776661 + 0.3333333334 Combine like terms: -2.260776661 + 0.3333333334 = -1.9274433276 x = -1.9274433276 Simplifying x = -1.9274433276Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5941099944, -1.9274433276}Solution
x = {2.5941099944, -1.9274433276}
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