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Simplifying 16x2 + 32x + -110 = 0 Reorder the terms: -110 + 32x + 16x2 = 0 Solving -110 + 32x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + 16x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-55 + 16x + 8x2)' equal to zero and attempt to solve: Simplifying -55 + 16x + 8x2 = 0 Solving -55 + 16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.875 + 2x + x2 = 0 Move the constant term to the right: Add '6.875' to each side of the equation. -6.875 + 2x + 6.875 + x2 = 0 + 6.875 Reorder the terms: -6.875 + 6.875 + 2x + x2 = 0 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + 2x + x2 = 0 + 6.875 2x + x2 = 0 + 6.875 Combine like terms: 0 + 6.875 = 6.875 2x + x2 = 6.875 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 = 6.875 + 1 Reorder the terms: 1 + 2x + x2 = 6.875 + 1 Combine like terms: 6.875 + 1 = 7.875 1 + 2x + x2 = 7.875 Factor a perfect square on the left side: (x + 1)(x + 1) = 7.875 Calculate the square root of the right side: 2.80624304 Break this problem into two subproblems by setting (x + 1) equal to 2.80624304 and -2.80624304.Subproblem 1
x + 1 = 2.80624304 Simplifying x + 1 = 2.80624304 Reorder the terms: 1 + x = 2.80624304 Solving 1 + x = 2.80624304 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 = 2.80624304 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.80624304 + -1 x = 2.80624304 + -1 Combine like terms: 2.80624304 + -1 = 1.80624304 x = 1.80624304 Simplifying x = 1.80624304Subproblem 2
x + 1 = -2.80624304 Simplifying x + 1 = -2.80624304 Reorder the terms: 1 + x = -2.80624304 Solving 1 + x = -2.80624304 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 = -2.80624304 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.80624304 + -1 x = -2.80624304 + -1 Combine like terms: -2.80624304 + -1 = -3.80624304 x = -3.80624304 Simplifying x = -3.80624304Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.80624304, -3.80624304}Solution
x = {1.80624304, -3.80624304}
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