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Simplifying -4x2 + 12 = -6x + -8 Reorder the terms: 12 + -4x2 = -6x + -8 Reorder the terms: 12 + -4x2 = -8 + -6x Solving 12 + -4x2 = -8 + -6x Solving for variable 'x'. Reorder the terms: 12 + 8 + 6x + -4x2 = -8 + -6x + 8 + 6x Combine like terms: 12 + 8 = 20 20 + 6x + -4x2 = -8 + -6x + 8 + 6x Reorder the terms: 20 + 6x + -4x2 = -8 + 8 + -6x + 6x Combine like terms: -8 + 8 = 0 20 + 6x + -4x2 = 0 + -6x + 6x 20 + 6x + -4x2 = -6x + 6x Combine like terms: -6x + 6x = 0 20 + 6x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 3x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 3x + -2x2)' equal to zero and attempt to solve: Simplifying 10 + 3x + -2x2 = 0 Solving 10 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5 + -1.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -1.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1.5x + x2 = 0 + 5 -1.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1.5x + x2 = 5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 5 + 0.5625 Combine like terms: 5 + 0.5625 = 5.5625 0.5625 + -1.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + -0.75) equal to 2.358495283 and -2.358495283.Subproblem 1
x + -0.75 = 2.358495283 Simplifying x + -0.75 = 2.358495283 Reorder the terms: -0.75 + x = 2.358495283 Solving -0.75 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.358495283 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.358495283 + 0.75 x = 2.358495283 + 0.75 Combine like terms: 2.358495283 + 0.75 = 3.108495283 x = 3.108495283 Simplifying x = 3.108495283Subproblem 2
x + -0.75 = -2.358495283 Simplifying x + -0.75 = -2.358495283 Reorder the terms: -0.75 + x = -2.358495283 Solving -0.75 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.358495283 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.358495283 + 0.75 x = -2.358495283 + 0.75 Combine like terms: -2.358495283 + 0.75 = -1.608495283 x = -1.608495283 Simplifying x = -1.608495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.108495283, -1.608495283}Solution
x = {3.108495283, -1.608495283}
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