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Simplifying -2x(x + -3) + 4x = -1(-1x + 1) Reorder the terms: -2x(-3 + x) + 4x = -1(-1x + 1) (-3 * -2x + x * -2x) + 4x = -1(-1x + 1) (6x + -2x2) + 4x = -1(-1x + 1) Reorder the terms: 6x + 4x + -2x2 = -1(-1x + 1) Combine like terms: 6x + 4x = 10x 10x + -2x2 = -1(-1x + 1) Reorder the terms: 10x + -2x2 = -1(1 + -1x) 10x + -2x2 = (1 * -1 + -1x * -1) 10x + -2x2 = (-1 + 1x) Solving 10x + -2x2 = -1 + 1x Solving for variable 'x'. Reorder the terms: 1 + 10x + -1x + -2x2 = -1 + 1x + 1 + -1x Combine like terms: 10x + -1x = 9x 1 + 9x + -2x2 = -1 + 1x + 1 + -1x Reorder the terms: 1 + 9x + -2x2 = -1 + 1 + 1x + -1x Combine like terms: -1 + 1 = 0 1 + 9x + -2x2 = 0 + 1x + -1x 1 + 9x + -2x2 = 1x + -1x Combine like terms: 1x + -1x = 0 1 + 9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -4.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -4.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -4.5x + x2 = 0 + 0.5 -4.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -4.5x + x2 = 0.5 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 = 0.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 0.5 + 5.0625 Combine like terms: 0.5 + 5.0625 = 5.5625 5.0625 + -4.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + -2.25) equal to 2.358495283 and -2.358495283.Subproblem 1
x + -2.25 = 2.358495283 Simplifying x + -2.25 = 2.358495283 Reorder the terms: -2.25 + x = 2.358495283 Solving -2.25 + x = 2.358495283 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 = 2.358495283 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.358495283 + 2.25 x = 2.358495283 + 2.25 Combine like terms: 2.358495283 + 2.25 = 4.608495283 x = 4.608495283 Simplifying x = 4.608495283Subproblem 2
x + -2.25 = -2.358495283 Simplifying x + -2.25 = -2.358495283 Reorder the terms: -2.25 + x = -2.358495283 Solving -2.25 + x = -2.358495283 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 = -2.358495283 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.358495283 + 2.25 x = -2.358495283 + 2.25 Combine like terms: -2.358495283 + 2.25 = -0.108495283 x = -0.108495283 Simplifying x = -0.108495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.608495283, -0.108495283}
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