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Simplifying 4x2 + 40x + -90 = 0 Reorder the terms: -90 + 40x + 4x2 = 0 Solving -90 + 40x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + 20x + 2x2) = 0 Ignore the factor 2.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 = 47.5 25 + 10x + x2 = 47.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 47.5 Calculate the square root of the right side: 6.892024376 Break this problem into two subproblems by setting (x + 5) equal to 6.892024376 and -6.892024376.Subproblem 1
x + 5 = 6.892024376 Simplifying x + 5 = 6.892024376 Reorder the terms: 5 + x = 6.892024376 Solving 5 + x = 6.892024376 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 = 6.892024376 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.892024376 + -5 x = 6.892024376 + -5 Combine like terms: 6.892024376 + -5 = 1.892024376 x = 1.892024376 Simplifying x = 1.892024376Subproblem 2
x + 5 = -6.892024376 Simplifying x + 5 = -6.892024376 Reorder the terms: 5 + x = -6.892024376 Solving 5 + x = -6.892024376 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 = -6.892024376 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.892024376 + -5 x = -6.892024376 + -5 Combine like terms: -6.892024376 + -5 = -11.892024376 x = -11.892024376 Simplifying x = -11.892024376Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.892024376, -11.892024376}Solution
x = {1.892024376, -11.892024376}
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