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Simplifying 40x2 + -156x + -76 = 0 Reorder the terms: -76 + -156x + 40x2 = 0 Solving -76 + -156x + 40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-19 + -39x + 10x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-19 + -39x + 10x2)' equal to zero and attempt to solve: Simplifying -19 + -39x + 10x2 = 0 Solving -19 + -39x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.9 + -3.9x + x2 = 0.0 Move the constant term to the right: Add '1.9' to each side of the equation. -1.9 + -3.9x + 1.9 + x2 = 0.0 + 1.9 Reorder the terms: -1.9 + 1.9 + -3.9x + x2 = 0.0 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + -3.9x + x2 = 0.0 + 1.9 -3.9x + x2 = 0.0 + 1.9 Combine like terms: 0.0 + 1.9 = 1.9 -3.9x + x2 = 1.9 The x term is -3.9x. Take half its coefficient (-1.95). Square it (3.8025) and add it to both sides. Add '3.8025' to each side of the equation. -3.9x + 3.8025 + x2 = 1.9 + 3.8025 Reorder the terms: 3.8025 + -3.9x + x2 = 1.9 + 3.8025 Combine like terms: 1.9 + 3.8025 = 5.7025 3.8025 + -3.9x + x2 = 5.7025 Factor a perfect square on the left side: (x + -1.95)(x + -1.95) = 5.7025 Calculate the square root of the right side: 2.387990787 Break this problem into two subproblems by setting (x + -1.95) equal to 2.387990787 and -2.387990787.Subproblem 1
x + -1.95 = 2.387990787 Simplifying x + -1.95 = 2.387990787 Reorder the terms: -1.95 + x = 2.387990787 Solving -1.95 + x = 2.387990787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.95' to each side of the equation. -1.95 + 1.95 + x = 2.387990787 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + x = 2.387990787 + 1.95 x = 2.387990787 + 1.95 Combine like terms: 2.387990787 + 1.95 = 4.337990787 x = 4.337990787 Simplifying x = 4.337990787Subproblem 2
x + -1.95 = -2.387990787 Simplifying x + -1.95 = -2.387990787 Reorder the terms: -1.95 + x = -2.387990787 Solving -1.95 + x = -2.387990787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.95' to each side of the equation. -1.95 + 1.95 + x = -2.387990787 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + x = -2.387990787 + 1.95 x = -2.387990787 + 1.95 Combine like terms: -2.387990787 + 1.95 = -0.437990787 x = -0.437990787 Simplifying x = -0.437990787Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.337990787, -0.437990787}Solution
x = {4.337990787, -0.437990787}
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