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Simplifying 2x2 + 10x = 180 Reorder the terms: 10x + 2x2 = 180 Solving 10x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 10x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + 5x + x2)' equal to zero and attempt to solve: Simplifying -90 + 5x + x2 = 0 Solving -90 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 5x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 5x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 5x + x2 = 0 + 90 5x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 5x + x2 = 90 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 90 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 90 + 6.25 Combine like terms: 90 + 6.25 = 96.25 6.25 + 5x + x2 = 96.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + 2.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + 2.5 = 9.810708435 Simplifying x + 2.5 = 9.810708435 Reorder the terms: 2.5 + x = 9.810708435 Solving 2.5 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 9.810708435 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 9.810708435 + -2.5 x = 9.810708435 + -2.5 Combine like terms: 9.810708435 + -2.5 = 7.310708435 x = 7.310708435 Simplifying x = 7.310708435Subproblem 2
x + 2.5 = -9.810708435 Simplifying x + 2.5 = -9.810708435 Reorder the terms: 2.5 + x = -9.810708435 Solving 2.5 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -9.810708435 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -9.810708435 + -2.5 x = -9.810708435 + -2.5 Combine like terms: -9.810708435 + -2.5 = -12.310708435 x = -12.310708435 Simplifying x = -12.310708435Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.310708435, -12.310708435}Solution
x = {7.310708435, -12.310708435}
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