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Simplifying 180 = 2x2 + 4x Reorder the terms: 180 = 4x + 2x2 Solving 180 = 4x + 2x2 Solving for variable 'x'. Reorder the terms: 180 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 180 + -4x + -2x2 = 0 + 2x2 + -2x2 180 + -4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 180 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(90 + -2x + -1x2)' equal to zero and attempt to solve: Simplifying 90 + -2x + -1x2 = 0 Solving 90 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -90 + 2x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 2x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 2x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 2x + x2 = 0 + 90 2x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 2x + x2 = 90 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 90 + 1 Reorder the terms: 1 + 2x + x2 = 90 + 1 Combine like terms: 90 + 1 = 91 1 + 2x + x2 = 91 Factor a perfect square on the left side: (x + 1)(x + 1) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + 1) equal to 9.539392014 and -9.539392014.Subproblem 1
x + 1 = 9.539392014 Simplifying x + 1 = 9.539392014 Reorder the terms: 1 + x = 9.539392014 Solving 1 + x = 9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 9.539392014 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.539392014 + -1 x = 9.539392014 + -1 Combine like terms: 9.539392014 + -1 = 8.539392014 x = 8.539392014 Simplifying x = 8.539392014Subproblem 2
x + 1 = -9.539392014 Simplifying x + 1 = -9.539392014 Reorder the terms: 1 + x = -9.539392014 Solving 1 + x = -9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -9.539392014 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.539392014 + -1 x = -9.539392014 + -1 Combine like terms: -9.539392014 + -1 = -10.539392014 x = -10.539392014 Simplifying x = -10.539392014Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.539392014, -10.539392014}Solution
x = {8.539392014, -10.539392014}
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