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Simplifying 128 = (x + -4)(x + -4)(3) Reorder the terms: 128 = (-4 + x)(x + -4)(3) Reorder the terms: 128 = (-4 + x)(-4 + x)(3) Reorder the terms for easier multiplication: 128 = 3(-4 + x)(-4 + x) Multiply (-4 + x) * (-4 + x) 128 = 3(-4(-4 + x) + x(-4 + x)) 128 = 3((-4 * -4 + x * -4) + x(-4 + x)) 128 = 3((16 + -4x) + x(-4 + x)) 128 = 3(16 + -4x + (-4 * x + x * x)) 128 = 3(16 + -4x + (-4x + x2)) Combine like terms: -4x + -4x = -8x 128 = 3(16 + -8x + x2) 128 = (16 * 3 + -8x * 3 + x2 * 3) 128 = (48 + -24x + 3x2) Solving 128 = 48 + -24x + 3x2 Solving for variable 'x'. Combine like terms: 128 + -48 = 80 80 + 24x + -3x2 = 48 + -24x + 3x2 + -48 + 24x + -3x2 Reorder the terms: 80 + 24x + -3x2 = 48 + -48 + -24x + 24x + 3x2 + -3x2 Combine like terms: 48 + -48 = 0 80 + 24x + -3x2 = 0 + -24x + 24x + 3x2 + -3x2 80 + 24x + -3x2 = -24x + 24x + 3x2 + -3x2 Combine like terms: -24x + 24x = 0 80 + 24x + -3x2 = 0 + 3x2 + -3x2 80 + 24x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 80 + 24x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -26.66666667 + -8x + x2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + -8x + 26.66666667 + x2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + -8x + x2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + -8x + x2 = 0 + 26.66666667 -8x + x2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 -8x + x2 = 26.66666667 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 26.66666667 + 16 Reorder the terms: 16 + -8x + x2 = 26.66666667 + 16 Combine like terms: 26.66666667 + 16 = 42.66666667 16 + -8x + x2 = 42.66666667 Factor a perfect square on the left side: (x + -4)(x + -4) = 42.66666667 Calculate the square root of the right side: 6.531972648 Break this problem into two subproblems by setting (x + -4) equal to 6.531972648 and -6.531972648.Subproblem 1
x + -4 = 6.531972648 Simplifying x + -4 = 6.531972648 Reorder the terms: -4 + x = 6.531972648 Solving -4 + x = 6.531972648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 6.531972648 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.531972648 + 4 x = 6.531972648 + 4 Combine like terms: 6.531972648 + 4 = 10.531972648 x = 10.531972648 Simplifying x = 10.531972648Subproblem 2
x + -4 = -6.531972648 Simplifying x + -4 = -6.531972648 Reorder the terms: -4 + x = -6.531972648 Solving -4 + x = -6.531972648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -6.531972648 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.531972648 + 4 x = -6.531972648 + 4 Combine like terms: -6.531972648 + 4 = -2.531972648 x = -2.531972648 Simplifying x = -2.531972648Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.531972648, -2.531972648}
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