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Simplifying 9(x + -4)(x + 4) = (x + 4)(x + -7) + 33 Reorder the terms: 9(-4 + x)(x + 4) = (x + 4)(x + -7) + 33 Reorder the terms: 9(-4 + x)(4 + x) = (x + 4)(x + -7) + 33 Multiply (-4 + x) * (4 + x) 9(-4(4 + x) + x(4 + x)) = (x + 4)(x + -7) + 33 9((4 * -4 + x * -4) + x(4 + x)) = (x + 4)(x + -7) + 33 9((-16 + -4x) + x(4 + x)) = (x + 4)(x + -7) + 33 9(-16 + -4x + (4 * x + x * x)) = (x + 4)(x + -7) + 33 9(-16 + -4x + (4x + x2)) = (x + 4)(x + -7) + 33 Combine like terms: -4x + 4x = 0 9(-16 + 0 + x2) = (x + 4)(x + -7) + 33 9(-16 + x2) = (x + 4)(x + -7) + 33 (-16 * 9 + x2 * 9) = (x + 4)(x + -7) + 33 (-144 + 9x2) = (x + 4)(x + -7) + 33 Reorder the terms: -144 + 9x2 = (4 + x)(x + -7) + 33 Reorder the terms: -144 + 9x2 = (4 + x)(-7 + x) + 33 Multiply (4 + x) * (-7 + x) -144 + 9x2 = (4(-7 + x) + x(-7 + x)) + 33 -144 + 9x2 = ((-7 * 4 + x * 4) + x(-7 + x)) + 33 -144 + 9x2 = ((-28 + 4x) + x(-7 + x)) + 33 -144 + 9x2 = (-28 + 4x + (-7 * x + x * x)) + 33 -144 + 9x2 = (-28 + 4x + (-7x + x2)) + 33 Combine like terms: 4x + -7x = -3x -144 + 9x2 = (-28 + -3x + x2) + 33 Reorder the terms: -144 + 9x2 = -28 + 33 + -3x + x2 Combine like terms: -28 + 33 = 5 -144 + 9x2 = 5 + -3x + x2 Solving -144 + 9x2 = 5 + -3x + x2 Solving for variable 'x'. Reorder the terms: -144 + -5 + 3x + 9x2 + -1x2 = 5 + -3x + x2 + -5 + 3x + -1x2 Combine like terms: -144 + -5 = -149 -149 + 3x + 9x2 + -1x2 = 5 + -3x + x2 + -5 + 3x + -1x2 Combine like terms: 9x2 + -1x2 = 8x2 -149 + 3x + 8x2 = 5 + -3x + x2 + -5 + 3x + -1x2 Reorder the terms: -149 + 3x + 8x2 = 5 + -5 + -3x + 3x + x2 + -1x2 Combine like terms: 5 + -5 = 0 -149 + 3x + 8x2 = 0 + -3x + 3x + x2 + -1x2 -149 + 3x + 8x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 -149 + 3x + 8x2 = 0 + x2 + -1x2 -149 + 3x + 8x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -149 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -18.625 + 0.375x + x2 = 0 Move the constant term to the right: Add '18.625' to each side of the equation. -18.625 + 0.375x + 18.625 + x2 = 0 + 18.625 Reorder the terms: -18.625 + 18.625 + 0.375x + x2 = 0 + 18.625 Combine like terms: -18.625 + 18.625 = 0.000 0.000 + 0.375x + x2 = 0 + 18.625 0.375x + x2 = 0 + 18.625 Combine like terms: 0 + 18.625 = 18.625 0.375x + x2 = 18.625 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 18.625 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 18.625 + 0.03515625 Combine like terms: 18.625 + 0.03515625 = 18.66015625 0.03515625 + 0.375x + x2 = 18.66015625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 18.66015625 Calculate the square root of the right side: 4.319740299 Break this problem into two subproblems by setting (x + 0.1875) equal to 4.319740299 and -4.319740299.Subproblem 1
x + 0.1875 = 4.319740299 Simplifying x + 0.1875 = 4.319740299 Reorder the terms: 0.1875 + x = 4.319740299 Solving 0.1875 + x = 4.319740299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 4.319740299 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 4.319740299 + -0.1875 x = 4.319740299 + -0.1875 Combine like terms: 4.319740299 + -0.1875 = 4.132240299 x = 4.132240299 Simplifying x = 4.132240299Subproblem 2
x + 0.1875 = -4.319740299 Simplifying x + 0.1875 = -4.319740299 Reorder the terms: 0.1875 + x = -4.319740299 Solving 0.1875 + x = -4.319740299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -4.319740299 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -4.319740299 + -0.1875 x = -4.319740299 + -0.1875 Combine like terms: -4.319740299 + -0.1875 = -4.507240299 x = -4.507240299 Simplifying x = -4.507240299Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.132240299, -4.507240299}
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