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Simplifying 0 = 2x2 + 20x + 45 Reorder the terms: 0 = 45 + 20x + 2x2 Solving 0 = 45 + 20x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -45 = -45 -45 + -20x + -2x2 = 45 + 20x + 2x2 + -45 + -20x + -2x2 Reorder the terms: -45 + -20x + -2x2 = 45 + -45 + 20x + -20x + 2x2 + -2x2 Combine like terms: 45 + -45 = 0 -45 + -20x + -2x2 = 0 + 20x + -20x + 2x2 + -2x2 -45 + -20x + -2x2 = 20x + -20x + 2x2 + -2x2 Combine like terms: 20x + -20x = 0 -45 + -20x + -2x2 = 0 + 2x2 + -2x2 -45 + -20x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -45 + -20x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(45 + 20x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(45 + 20x + 2x2)' equal to zero and attempt to solve: Simplifying 45 + 20x + 2x2 = 0 Solving 45 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + 10x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + 10x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + 10x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + 10x + x2 = 0 + -22.5 10x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 10x + x2 = -22.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -22.5 + 25 Reorder the terms: 25 + 10x + x2 = -22.5 + 25 Combine like terms: -22.5 + 25 = 2.5 25 + 10x + x2 = 2.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (x + 5) equal to 1.58113883 and -1.58113883.Subproblem 1
x + 5 = 1.58113883 Simplifying x + 5 = 1.58113883 Reorder the terms: 5 + x = 1.58113883 Solving 5 + x = 1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 1.58113883 + -5 Combine like terms: 5 + -5 = 0 0 + x = 1.58113883 + -5 x = 1.58113883 + -5 Combine like terms: 1.58113883 + -5 = -3.41886117 x = -3.41886117 Simplifying x = -3.41886117Subproblem 2
x + 5 = -1.58113883 Simplifying x + 5 = -1.58113883 Reorder the terms: 5 + x = -1.58113883 Solving 5 + x = -1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -1.58113883 + -5 Combine like terms: 5 + -5 = 0 0 + x = -1.58113883 + -5 x = -1.58113883 + -5 Combine like terms: -1.58113883 + -5 = -6.58113883 x = -6.58113883 Simplifying x = -6.58113883Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.41886117, -6.58113883}Solution
x = {-3.41886117, -6.58113883}
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