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Simplifying -2x2 + -4x = -74 Reorder the terms: -4x + -2x2 = -74 Solving -4x + -2x2 = -74 Solving for variable 'x'. Reorder the terms: 74 + -4x + -2x2 = -74 + 74 Combine like terms: -74 + 74 = 0 74 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(37 + -2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(37 + -2x + -1x2)' equal to zero and attempt to solve: Simplifying 37 + -2x + -1x2 = 0 Solving 37 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -37 + 2x + x2 = 0 Move the constant term to the right: Add '37' to each side of the equation. -37 + 2x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + 2x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 2x + x2 = 0 + 37 2x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 2x + x2 = 37 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 = 37 + 1 Reorder the terms: 1 + 2x + x2 = 37 + 1 Combine like terms: 37 + 1 = 38 1 + 2x + x2 = 38 Factor a perfect square on the left side: (x + 1)(x + 1) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + 1) equal to 6.164414003 and -6.164414003.Subproblem 1
x + 1 = 6.164414003 Simplifying x + 1 = 6.164414003 Reorder the terms: 1 + x = 6.164414003 Solving 1 + x = 6.164414003 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 = 6.164414003 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.164414003 + -1 x = 6.164414003 + -1 Combine like terms: 6.164414003 + -1 = 5.164414003 x = 5.164414003 Simplifying x = 5.164414003Subproblem 2
x + 1 = -6.164414003 Simplifying x + 1 = -6.164414003 Reorder the terms: 1 + x = -6.164414003 Solving 1 + x = -6.164414003 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 = -6.164414003 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.164414003 + -1 x = -6.164414003 + -1 Combine like terms: -6.164414003 + -1 = -7.164414003 x = -7.164414003 Simplifying x = -7.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.164414003, -7.164414003}Solution
x = {5.164414003, -7.164414003}
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