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Simplifying -3(2x2 + -1x + 2) + -4(-3x2 + -3x + 6) = 0 Reorder the terms: -3(2 + -1x + 2x2) + -4(-3x2 + -3x + 6) = 0 (2 * -3 + -1x * -3 + 2x2 * -3) + -4(-3x2 + -3x + 6) = 0 (-6 + 3x + -6x2) + -4(-3x2 + -3x + 6) = 0 Reorder the terms: -6 + 3x + -6x2 + -4(6 + -3x + -3x2) = 0 -6 + 3x + -6x2 + (6 * -4 + -3x * -4 + -3x2 * -4) = 0 -6 + 3x + -6x2 + (-24 + 12x + 12x2) = 0 Reorder the terms: -6 + -24 + 3x + 12x + -6x2 + 12x2 = 0 Combine like terms: -6 + -24 = -30 -30 + 3x + 12x + -6x2 + 12x2 = 0 Combine like terms: 3x + 12x = 15x -30 + 15x + -6x2 + 12x2 = 0 Combine like terms: -6x2 + 12x2 = 6x2 -30 + 15x + 6x2 = 0 Solving -30 + 15x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + 5x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying -10 + 5x + 2x2 = 0 Solving -10 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 2.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.5x + x2 = 0 + 5 2.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2.5x + x2 = 5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 5 + 1.5625 Combine like terms: 5 + 1.5625 = 6.5625 1.5625 + 2.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + 1.25) equal to 2.561737691 and -2.561737691.Subproblem 1
x + 1.25 = 2.561737691 Simplifying x + 1.25 = 2.561737691 Reorder the terms: 1.25 + x = 2.561737691 Solving 1.25 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.561737691 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.561737691 + -1.25 x = 2.561737691 + -1.25 Combine like terms: 2.561737691 + -1.25 = 1.311737691 x = 1.311737691 Simplifying x = 1.311737691Subproblem 2
x + 1.25 = -2.561737691 Simplifying x + 1.25 = -2.561737691 Reorder the terms: 1.25 + x = -2.561737691 Solving 1.25 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.561737691 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.561737691 + -1.25 x = -2.561737691 + -1.25 Combine like terms: -2.561737691 + -1.25 = -3.811737691 x = -3.811737691 Simplifying x = -3.811737691Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.311737691, -3.811737691}Solution
x = {1.311737691, -3.811737691}
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