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Simplifying (x + -4) + (x + -5)(x + 5) = 2(x + 2) + 24 Reorder the terms: (-4 + x) + (x + -5)(x + 5) = 2(x + 2) + 24 Remove parenthesis around (-4 + x) -4 + x + (x + -5)(x + 5) = 2(x + 2) + 24 Reorder the terms: -4 + x + (-5 + x)(x + 5) = 2(x + 2) + 24 Reorder the terms: -4 + x + (-5 + x)(5 + x) = 2(x + 2) + 24 Multiply (-5 + x) * (5 + x) -4 + x + (-5(5 + x) + x(5 + x)) = 2(x + 2) + 24 -4 + x + ((5 * -5 + x * -5) + x(5 + x)) = 2(x + 2) + 24 -4 + x + ((-25 + -5x) + x(5 + x)) = 2(x + 2) + 24 -4 + x + (-25 + -5x + (5 * x + x * x)) = 2(x + 2) + 24 -4 + x + (-25 + -5x + (5x + x2)) = 2(x + 2) + 24 Combine like terms: -5x + 5x = 0 -4 + x + (-25 + 0 + x2) = 2(x + 2) + 24 -4 + x + (-25 + x2) = 2(x + 2) + 24 Reorder the terms: -4 + -25 + x + x2 = 2(x + 2) + 24 Combine like terms: -4 + -25 = -29 -29 + x + x2 = 2(x + 2) + 24 Reorder the terms: -29 + x + x2 = 2(2 + x) + 24 -29 + x + x2 = (2 * 2 + x * 2) + 24 -29 + x + x2 = (4 + 2x) + 24 Reorder the terms: -29 + x + x2 = 4 + 24 + 2x Combine like terms: 4 + 24 = 28 -29 + x + x2 = 28 + 2x Solving -29 + x + x2 = 28 + 2x Solving for variable 'x'. Reorder the terms: -29 + -28 + x + -2x + x2 = 28 + 2x + -28 + -2x Combine like terms: -29 + -28 = -57 -57 + x + -2x + x2 = 28 + 2x + -28 + -2x Combine like terms: x + -2x = -1x -57 + -1x + x2 = 28 + 2x + -28 + -2x Reorder the terms: -57 + -1x + x2 = 28 + -28 + 2x + -2x Combine like terms: 28 + -28 = 0 -57 + -1x + x2 = 0 + 2x + -2x -57 + -1x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -57 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + -1x + 57 + x2 = 0 + 57 Reorder the terms: -57 + 57 + -1x + x2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + -1x + x2 = 0 + 57 -1x + x2 = 0 + 57 Combine like terms: 0 + 57 = 57 -1x + x2 = 57 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 57 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 57 + 0.25 Combine like terms: 57 + 0.25 = 57.25 0.25 + -1x + x2 = 57.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + -0.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + -0.5 = 7.566372975 Simplifying x + -0.5 = 7.566372975 Reorder the terms: -0.5 + x = 7.566372975 Solving -0.5 + x = 7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 7.566372975 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.566372975 + 0.5 x = 7.566372975 + 0.5 Combine like terms: 7.566372975 + 0.5 = 8.066372975 x = 8.066372975 Simplifying x = 8.066372975Subproblem 2
x + -0.5 = -7.566372975 Simplifying x + -0.5 = -7.566372975 Reorder the terms: -0.5 + x = -7.566372975 Solving -0.5 + x = -7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -7.566372975 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.566372975 + 0.5 x = -7.566372975 + 0.5 Combine like terms: -7.566372975 + 0.5 = -7.066372975 x = -7.066372975 Simplifying x = -7.066372975Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.066372975, -7.066372975}
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