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Simplifying (8x + -18) + (10x)(4x) = 180 Reorder the terms: (-18 + 8x) + (10x)(4x) = 180 Remove parenthesis around (-18 + 8x) -18 + 8x + (10x)(4x) = 180 Remove parenthesis around (10x) -18 + 8x + 10x(4x) = 180 Remove parenthesis around (4x) -18 + 8x + 10x * 4x = 180 Reorder the terms for easier multiplication: -18 + 8x + 10 * 4x * x = 180 Multiply 10 * 4 -18 + 8x + 40x * x = 180 Multiply x * x -18 + 8x + 40x2 = 180 Solving -18 + 8x + 40x2 = 180 Solving for variable 'x'. Reorder the terms: -18 + -180 + 8x + 40x2 = 180 + -180 Combine like terms: -18 + -180 = -198 -198 + 8x + 40x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -198 + 8x + 40x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-99 + 4x + 20x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-99 + 4x + 20x2)' equal to zero and attempt to solve: Simplifying -99 + 4x + 20x2 = 0 Solving -99 + 4x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -4.95 + 0.2x + x2 = 0.0 Move the constant term to the right: Add '4.95' to each side of the equation. -4.95 + 0.2x + 4.95 + x2 = 0.0 + 4.95 Reorder the terms: -4.95 + 4.95 + 0.2x + x2 = 0.0 + 4.95 Combine like terms: -4.95 + 4.95 = 0.00 0.00 + 0.2x + x2 = 0.0 + 4.95 0.2x + x2 = 0.0 + 4.95 Combine like terms: 0.0 + 4.95 = 4.95 0.2x + x2 = 4.95 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 4.95 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 4.95 + 0.01 Combine like terms: 4.95 + 0.01 = 4.96 0.01 + 0.2x + x2 = 4.96 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 4.96 Calculate the square root of the right side: 2.227105745 Break this problem into two subproblems by setting (x + 0.1) equal to 2.227105745 and -2.227105745.Subproblem 1
x + 0.1 = 2.227105745 Simplifying x + 0.1 = 2.227105745 Reorder the terms: 0.1 + x = 2.227105745 Solving 0.1 + x = 2.227105745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 2.227105745 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 2.227105745 + -0.1 x = 2.227105745 + -0.1 Combine like terms: 2.227105745 + -0.1 = 2.127105745 x = 2.127105745 Simplifying x = 2.127105745Subproblem 2
x + 0.1 = -2.227105745 Simplifying x + 0.1 = -2.227105745 Reorder the terms: 0.1 + x = -2.227105745 Solving 0.1 + x = -2.227105745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -2.227105745 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -2.227105745 + -0.1 x = -2.227105745 + -0.1 Combine like terms: -2.227105745 + -0.1 = -2.327105745 x = -2.327105745 Simplifying x = -2.327105745Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.127105745, -2.327105745}Solution
x = {2.127105745, -2.327105745}
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