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Simplifying (6x2 + -6x + 12) + (9x2 + 9x + -57) = 0 Reorder the terms: (12 + -6x + 6x2) + (9x2 + 9x + -57) = 0 Remove parenthesis around (12 + -6x + 6x2) 12 + -6x + 6x2 + (9x2 + 9x + -57) = 0 Reorder the terms: 12 + -6x + 6x2 + (-57 + 9x + 9x2) = 0 Remove parenthesis around (-57 + 9x + 9x2) 12 + -6x + 6x2 + -57 + 9x + 9x2 = 0 Reorder the terms: 12 + -57 + -6x + 9x + 6x2 + 9x2 = 0 Combine like terms: 12 + -57 = -45 -45 + -6x + 9x + 6x2 + 9x2 = 0 Combine like terms: -6x + 9x = 3x -45 + 3x + 6x2 + 9x2 = 0 Combine like terms: 6x2 + 9x2 = 15x2 -45 + 3x + 15x2 = 0 Solving -45 + 3x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-15 + x + 5x2)' equal to zero and attempt to solve: Simplifying -15 + x + 5x2 = 0 Solving -15 + x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + 0.2x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.2x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.2x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.2x + x2 = 0 + 3 0.2x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.2x + x2 = 3 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.2x + 0.25 + x2 = 3 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + 0.2x + x2 = 3.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 0.5 = 1.802775638 Simplifying x + 0.5 = 1.802775638 Reorder the terms: 0.5 + x = 1.802775638 Solving 0.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.802775638 + -0.5 x = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 x = 1.302775638 Simplifying x = 1.302775638Subproblem 2
x + 0.5 = -1.802775638 Simplifying x + 0.5 = -1.802775638 Reorder the terms: 0.5 + x = -1.802775638 Solving 0.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.802775638 + -0.5 x = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 x = -2.302775638 Simplifying x = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.302775638, -2.302775638}Solution
x = {1.302775638, -2.302775638}
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