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Simplifying 24 + -1x(x + 2) = 29 + 18x Reorder the terms: 24 + -1x(2 + x) = 29 + 18x 24 + (2 * -1x + x * -1x) = 29 + 18x 24 + (-2x + -1x2) = 29 + 18x Solving 24 + -2x + -1x2 = 29 + 18x Solving for variable 'x'. Reorder the terms: 24 + -29 + -2x + -18x + -1x2 = 29 + 18x + -29 + -18x Combine like terms: 24 + -29 = -5 -5 + -2x + -18x + -1x2 = 29 + 18x + -29 + -18x Combine like terms: -2x + -18x = -20x -5 + -20x + -1x2 = 29 + 18x + -29 + -18x Reorder the terms: -5 + -20x + -1x2 = 29 + -29 + 18x + -18x Combine like terms: 29 + -29 = 0 -5 + -20x + -1x2 = 0 + 18x + -18x -5 + -20x + -1x2 = 18x + -18x Combine like terms: 18x + -18x = 0 -5 + -20x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 20x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 20x + x2)' equal to zero and attempt to solve: Simplifying 5 + 20x + x2 = 0 Solving 5 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 20x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 20x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 20x + x2 = 0 + -5 20x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 20x + x2 = -5 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -5 + 100 Reorder the terms: 100 + 20x + x2 = -5 + 100 Combine like terms: -5 + 100 = 95 100 + 20x + x2 = 95 Factor a perfect square on the left side: (x + 10)(x + 10) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (x + 10) equal to 9.746794345 and -9.746794345.Subproblem 1
x + 10 = 9.746794345 Simplifying x + 10 = 9.746794345 Reorder the terms: 10 + x = 9.746794345 Solving 10 + x = 9.746794345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 9.746794345 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.746794345 + -10 x = 9.746794345 + -10 Combine like terms: 9.746794345 + -10 = -0.253205655 x = -0.253205655 Simplifying x = -0.253205655Subproblem 2
x + 10 = -9.746794345 Simplifying x + 10 = -9.746794345 Reorder the terms: 10 + x = -9.746794345 Solving 10 + x = -9.746794345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -9.746794345 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.746794345 + -10 x = -9.746794345 + -10 Combine like terms: -9.746794345 + -10 = -19.746794345 x = -19.746794345 Simplifying x = -19.746794345Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.253205655, -19.746794345}Solution
x = {-0.253205655, -19.746794345}
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