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Simplifying 12 + -10x = 4x2 + 8x Reorder the terms: 12 + -10x = 8x + 4x2 Solving 12 + -10x = 8x + 4x2 Solving for variable 'x'. Combine like terms: -10x + -8x = -18x 12 + -18x + -4x2 = 8x + 4x2 + -8x + -4x2 Reorder the terms: 12 + -18x + -4x2 = 8x + -8x + 4x2 + -4x2 Combine like terms: 8x + -8x = 0 12 + -18x + -4x2 = 0 + 4x2 + -4x2 12 + -18x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 12 + -18x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -9x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -9x + -2x2)' equal to zero and attempt to solve: Simplifying 6 + -9x + -2x2 = 0 Solving 6 + -9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3 + 4.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 4.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 4.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4.5x + x2 = 0 + 3 4.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 4.5x + x2 = 3 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 3 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 3 + 5.0625 Combine like terms: 3 + 5.0625 = 8.0625 5.0625 + 4.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + 2.25) equal to 2.839454173 and -2.839454173.Subproblem 1
x + 2.25 = 2.839454173 Simplifying x + 2.25 = 2.839454173 Reorder the terms: 2.25 + x = 2.839454173 Solving 2.25 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.839454173 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.839454173 + -2.25 x = 2.839454173 + -2.25 Combine like terms: 2.839454173 + -2.25 = 0.589454173 x = 0.589454173 Simplifying x = 0.589454173Subproblem 2
x + 2.25 = -2.839454173 Simplifying x + 2.25 = -2.839454173 Reorder the terms: 2.25 + x = -2.839454173 Solving 2.25 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.839454173 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.839454173 + -2.25 x = -2.839454173 + -2.25 Combine like terms: -2.839454173 + -2.25 = -5.089454173 x = -5.089454173 Simplifying x = -5.089454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.589454173, -5.089454173}Solution
x = {0.589454173, -5.089454173}
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