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Simplifying (x + -2)(x + 2) = 72 + -9x Reorder the terms: (-2 + x)(x + 2) = 72 + -9x Reorder the terms: (-2 + x)(2 + x) = 72 + -9x Multiply (-2 + x) * (2 + x) (-2(2 + x) + x(2 + x)) = 72 + -9x ((2 * -2 + x * -2) + x(2 + x)) = 72 + -9x ((-4 + -2x) + x(2 + x)) = 72 + -9x (-4 + -2x + (2 * x + x * x)) = 72 + -9x (-4 + -2x + (2x + x2)) = 72 + -9x Combine like terms: -2x + 2x = 0 (-4 + 0 + x2) = 72 + -9x (-4 + x2) = 72 + -9x Solving -4 + x2 = 72 + -9x Solving for variable 'x'. Reorder the terms: -4 + -72 + 9x + x2 = 72 + -9x + -72 + 9x Combine like terms: -4 + -72 = -76 -76 + 9x + x2 = 72 + -9x + -72 + 9x Reorder the terms: -76 + 9x + x2 = 72 + -72 + -9x + 9x Combine like terms: 72 + -72 = 0 -76 + 9x + x2 = 0 + -9x + 9x -76 + 9x + x2 = -9x + 9x Combine like terms: -9x + 9x = 0 -76 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 9x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + 9x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 9x + x2 = 0 + 76 9x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 9x + x2 = 76 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 = 76 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 76 + 20.25 Combine like terms: 76 + 20.25 = 96.25 20.25 + 9x + x2 = 96.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + 4.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + 4.5 = 9.810708435 Simplifying x + 4.5 = 9.810708435 Reorder the terms: 4.5 + x = 9.810708435 Solving 4.5 + x = 9.810708435 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 = 9.810708435 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 9.810708435 + -4.5 x = 9.810708435 + -4.5 Combine like terms: 9.810708435 + -4.5 = 5.310708435 x = 5.310708435 Simplifying x = 5.310708435Subproblem 2
x + 4.5 = -9.810708435 Simplifying x + 4.5 = -9.810708435 Reorder the terms: 4.5 + x = -9.810708435 Solving 4.5 + x = -9.810708435 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 = -9.810708435 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -9.810708435 + -4.5 x = -9.810708435 + -4.5 Combine like terms: -9.810708435 + -4.5 = -14.310708435 x = -14.310708435 Simplifying x = -14.310708435Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.310708435, -14.310708435}
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