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Simplifying 2(x + 2)(x + -3) + -3 = 4(x + 1)(x + -6) + 4 Reorder the terms: 2(2 + x)(x + -3) + -3 = 4(x + 1)(x + -6) + 4 Reorder the terms: 2(2 + x)(-3 + x) + -3 = 4(x + 1)(x + -6) + 4 Multiply (2 + x) * (-3 + x) 2(2(-3 + x) + x(-3 + x)) + -3 = 4(x + 1)(x + -6) + 4 2((-3 * 2 + x * 2) + x(-3 + x)) + -3 = 4(x + 1)(x + -6) + 4 2((-6 + 2x) + x(-3 + x)) + -3 = 4(x + 1)(x + -6) + 4 2(-6 + 2x + (-3 * x + x * x)) + -3 = 4(x + 1)(x + -6) + 4 2(-6 + 2x + (-3x + x2)) + -3 = 4(x + 1)(x + -6) + 4 Combine like terms: 2x + -3x = -1x 2(-6 + -1x + x2) + -3 = 4(x + 1)(x + -6) + 4 (-6 * 2 + -1x * 2 + x2 * 2) + -3 = 4(x + 1)(x + -6) + 4 (-12 + -2x + 2x2) + -3 = 4(x + 1)(x + -6) + 4 Reorder the terms: -12 + -3 + -2x + 2x2 = 4(x + 1)(x + -6) + 4 Combine like terms: -12 + -3 = -15 -15 + -2x + 2x2 = 4(x + 1)(x + -6) + 4 Reorder the terms: -15 + -2x + 2x2 = 4(1 + x)(x + -6) + 4 Reorder the terms: -15 + -2x + 2x2 = 4(1 + x)(-6 + x) + 4 Multiply (1 + x) * (-6 + x) -15 + -2x + 2x2 = 4(1(-6 + x) + x(-6 + x)) + 4 -15 + -2x + 2x2 = 4((-6 * 1 + x * 1) + x(-6 + x)) + 4 -15 + -2x + 2x2 = 4((-6 + 1x) + x(-6 + x)) + 4 -15 + -2x + 2x2 = 4(-6 + 1x + (-6 * x + x * x)) + 4 -15 + -2x + 2x2 = 4(-6 + 1x + (-6x + x2)) + 4 Combine like terms: 1x + -6x = -5x -15 + -2x + 2x2 = 4(-6 + -5x + x2) + 4 -15 + -2x + 2x2 = (-6 * 4 + -5x * 4 + x2 * 4) + 4 -15 + -2x + 2x2 = (-24 + -20x + 4x2) + 4 Reorder the terms: -15 + -2x + 2x2 = -24 + 4 + -20x + 4x2 Combine like terms: -24 + 4 = -20 -15 + -2x + 2x2 = -20 + -20x + 4x2 Solving -15 + -2x + 2x2 = -20 + -20x + 4x2 Solving for variable 'x'. Reorder the terms: -15 + 20 + -2x + 20x + 2x2 + -4x2 = -20 + -20x + 4x2 + 20 + 20x + -4x2 Combine like terms: -15 + 20 = 5 5 + -2x + 20x + 2x2 + -4x2 = -20 + -20x + 4x2 + 20 + 20x + -4x2 Combine like terms: -2x + 20x = 18x 5 + 18x + 2x2 + -4x2 = -20 + -20x + 4x2 + 20 + 20x + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 5 + 18x + -2x2 = -20 + -20x + 4x2 + 20 + 20x + -4x2 Reorder the terms: 5 + 18x + -2x2 = -20 + 20 + -20x + 20x + 4x2 + -4x2 Combine like terms: -20 + 20 = 0 5 + 18x + -2x2 = 0 + -20x + 20x + 4x2 + -4x2 5 + 18x + -2x2 = -20x + 20x + 4x2 + -4x2 Combine like terms: -20x + 20x = 0 5 + 18x + -2x2 = 0 + 4x2 + -4x2 5 + 18x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 5 + 18x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + -9x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -9x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -9x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -9x + x2 = 0 + 2.5 -9x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -9x + x2 = 2.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 2.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 2.5 + 20.25 Combine like terms: 2.5 + 20.25 = 22.75 20.25 + -9x + x2 = 22.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (x + -4.5) equal to 4.769696007 and -4.769696007.Subproblem 1
x + -4.5 = 4.769696007 Simplifying x + -4.5 = 4.769696007 Reorder the terms: -4.5 + x = 4.769696007 Solving -4.5 + x = 4.769696007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.769696007 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.769696007 + 4.5 x = 4.769696007 + 4.5 Combine like terms: 4.769696007 + 4.5 = 9.269696007 x = 9.269696007 Simplifying x = 9.269696007Subproblem 2
x + -4.5 = -4.769696007 Simplifying x + -4.5 = -4.769696007 Reorder the terms: -4.5 + x = -4.769696007 Solving -4.5 + x = -4.769696007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.769696007 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.769696007 + 4.5 x = -4.769696007 + 4.5 Combine like terms: -4.769696007 + 4.5 = -0.269696007 x = -0.269696007 Simplifying x = -0.269696007Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.269696007, -0.269696007}
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