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Simplifying 40x2 + 80x + -90 = 0 Reorder the terms: -90 + 80x + 40x2 = 0 Solving -90 + 80x + 40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-9 + 8x + 4x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-9 + 8x + 4x2)' equal to zero and attempt to solve: Simplifying -9 + 8x + 4x2 = 0 Solving -9 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 2x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 2x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 2x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 2x + x2 = 0 + 2.25 2x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 2x + x2 = 2.25 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 = 2.25 + 1 Reorder the terms: 1 + 2x + x2 = 2.25 + 1 Combine like terms: 2.25 + 1 = 3.25 1 + 2x + x2 = 3.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 1) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 1 = 1.802775638 Simplifying x + 1 = 1.802775638 Reorder the terms: 1 + x = 1.802775638 Solving 1 + x = 1.802775638 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 = 1.802775638 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.802775638 + -1 x = 1.802775638 + -1 Combine like terms: 1.802775638 + -1 = 0.802775638 x = 0.802775638 Simplifying x = 0.802775638Subproblem 2
x + 1 = -1.802775638 Simplifying x + 1 = -1.802775638 Reorder the terms: 1 + x = -1.802775638 Solving 1 + x = -1.802775638 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 = -1.802775638 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.802775638 + -1 x = -1.802775638 + -1 Combine like terms: -1.802775638 + -1 = -2.802775638 x = -2.802775638 Simplifying x = -2.802775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.802775638, -2.802775638}Solution
x = {0.802775638, -2.802775638}
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