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Simplifying 64 + 9(x + 2)(x + 2) = 84 Reorder the terms: 64 + 9(2 + x)(x + 2) = 84 Reorder the terms: 64 + 9(2 + x)(2 + x) = 84 Multiply (2 + x) * (2 + x) 64 + 9(2(2 + x) + x(2 + x)) = 84 64 + 9((2 * 2 + x * 2) + x(2 + x)) = 84 64 + 9((4 + 2x) + x(2 + x)) = 84 64 + 9(4 + 2x + (2 * x + x * x)) = 84 64 + 9(4 + 2x + (2x + x2)) = 84 Combine like terms: 2x + 2x = 4x 64 + 9(4 + 4x + x2) = 84 64 + (4 * 9 + 4x * 9 + x2 * 9) = 84 64 + (36 + 36x + 9x2) = 84 Combine like terms: 64 + 36 = 100 100 + 36x + 9x2 = 84 Solving 100 + 36x + 9x2 = 84 Solving for variable 'x'. Reorder the terms: 100 + -84 + 36x + 9x2 = 84 + -84 Combine like terms: 100 + -84 = 16 16 + 36x + 9x2 = 84 + -84 Combine like terms: 84 + -84 = 0 16 + 36x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.777777778 + 4x + x2 = 0 Move the constant term to the right: Add '-1.777777778' to each side of the equation. 1.777777778 + 4x + -1.777777778 + x2 = 0 + -1.777777778 Reorder the terms: 1.777777778 + -1.777777778 + 4x + x2 = 0 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + 4x + x2 = 0 + -1.777777778 4x + x2 = 0 + -1.777777778 Combine like terms: 0 + -1.777777778 = -1.777777778 4x + x2 = -1.777777778 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -1.777777778 + 4 Reorder the terms: 4 + 4x + x2 = -1.777777778 + 4 Combine like terms: -1.777777778 + 4 = 2.222222222 4 + 4x + x2 = 2.222222222 Factor a perfect square on the left side: (x + 2)(x + 2) = 2.222222222 Calculate the square root of the right side: 1.490711985 Break this problem into two subproblems by setting (x + 2) equal to 1.490711985 and -1.490711985.Subproblem 1
x + 2 = 1.490711985 Simplifying x + 2 = 1.490711985 Reorder the terms: 2 + x = 1.490711985 Solving 2 + x = 1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.490711985 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.490711985 + -2 x = 1.490711985 + -2 Combine like terms: 1.490711985 + -2 = -0.509288015 x = -0.509288015 Simplifying x = -0.509288015Subproblem 2
x + 2 = -1.490711985 Simplifying x + 2 = -1.490711985 Reorder the terms: 2 + x = -1.490711985 Solving 2 + x = -1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.490711985 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.490711985 + -2 x = -1.490711985 + -2 Combine like terms: -1.490711985 + -2 = -3.490711985 x = -3.490711985 Simplifying x = -3.490711985Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.509288015, -3.490711985}
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