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Simplifying -5x2 + -44x = 12 Reorder the terms: -44x + -5x2 = 12 Solving -44x + -5x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -44x + -5x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -44x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 44x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 44x + 5x2)' equal to zero and attempt to solve: Simplifying 12 + 44x + 5x2 = 0 Solving 12 + 44x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 8.8x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 8.8x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 8.8x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 8.8x + x2 = 0 + -2.4 8.8x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 8.8x + x2 = -2.4 The x term is 8.8x. Take half its coefficient (4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. 8.8x + 19.36 + x2 = -2.4 + 19.36 Reorder the terms: 19.36 + 8.8x + x2 = -2.4 + 19.36 Combine like terms: -2.4 + 19.36 = 16.96 19.36 + 8.8x + x2 = 16.96 Factor a perfect square on the left side: (x + 4.4)(x + 4.4) = 16.96 Calculate the square root of the right side: 4.118252056 Break this problem into two subproblems by setting (x + 4.4) equal to 4.118252056 and -4.118252056.Subproblem 1
x + 4.4 = 4.118252056 Simplifying x + 4.4 = 4.118252056 Reorder the terms: 4.4 + x = 4.118252056 Solving 4.4 + x = 4.118252056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = 4.118252056 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = 4.118252056 + -4.4 x = 4.118252056 + -4.4 Combine like terms: 4.118252056 + -4.4 = -0.281747944 x = -0.281747944 Simplifying x = -0.281747944Subproblem 2
x + 4.4 = -4.118252056 Simplifying x + 4.4 = -4.118252056 Reorder the terms: 4.4 + x = -4.118252056 Solving 4.4 + x = -4.118252056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = -4.118252056 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = -4.118252056 + -4.4 x = -4.118252056 + -4.4 Combine like terms: -4.118252056 + -4.4 = -8.518252056 x = -8.518252056 Simplifying x = -8.518252056Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.281747944, -8.518252056}Solution
x = {-0.281747944, -8.518252056}
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