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Simplifying 200x2 + 300x + -80 = 0 Reorder the terms: -80 + 300x + 200x2 = 0 Solving -80 + 300x + 200x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '20'. 20(-4 + 15x + 10x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-4 + 15x + 10x2)' equal to zero and attempt to solve: Simplifying -4 + 15x + 10x2 = 0 Solving -4 + 15x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + 1.5x + x2 = 0.0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.5x + 0.4 + x2 = 0.0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.5x + x2 = 0.0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.5x + x2 = 0.0 + 0.4 1.5x + x2 = 0.0 + 0.4 Combine like terms: 0.0 + 0.4 = 0.4 1.5x + x2 = 0.4 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 0.4 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 0.4 + 0.5625 Combine like terms: 0.4 + 0.5625 = 0.9625 0.5625 + 1.5x + x2 = 0.9625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 0.9625 Calculate the square root of the right side: 0.981070844 Break this problem into two subproblems by setting (x + 0.75) equal to 0.981070844 and -0.981070844.Subproblem 1
x + 0.75 = 0.981070844 Simplifying x + 0.75 = 0.981070844 Reorder the terms: 0.75 + x = 0.981070844 Solving 0.75 + x = 0.981070844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 0.981070844 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.981070844 + -0.75 x = 0.981070844 + -0.75 Combine like terms: 0.981070844 + -0.75 = 0.231070844 x = 0.231070844 Simplifying x = 0.231070844Subproblem 2
x + 0.75 = -0.981070844 Simplifying x + 0.75 = -0.981070844 Reorder the terms: 0.75 + x = -0.981070844 Solving 0.75 + x = -0.981070844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -0.981070844 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.981070844 + -0.75 x = -0.981070844 + -0.75 Combine like terms: -0.981070844 + -0.75 = -1.731070844 x = -1.731070844 Simplifying x = -1.731070844Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.231070844, -1.731070844}Solution
x = {0.231070844, -1.731070844}
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