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Simplifying 8x(22 + -1x) = 198 (22 * 8x + -1x * 8x) = 198 (176x + -8x2) = 198 Solving 176x + -8x2 = 198 Solving for variable 'x'. Reorder the terms: -198 + 176x + -8x2 = 198 + -198 Combine like terms: 198 + -198 = 0 -198 + 176x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-99 + 88x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-99 + 88x + -4x2)' equal to zero and attempt to solve: Simplifying -99 + 88x + -4x2 = 0 Solving -99 + 88x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 24.75 + -22x + x2 = 0 Move the constant term to the right: Add '-24.75' to each side of the equation. 24.75 + -22x + -24.75 + x2 = 0 + -24.75 Reorder the terms: 24.75 + -24.75 + -22x + x2 = 0 + -24.75 Combine like terms: 24.75 + -24.75 = 0.00 0.00 + -22x + x2 = 0 + -24.75 -22x + x2 = 0 + -24.75 Combine like terms: 0 + -24.75 = -24.75 -22x + x2 = -24.75 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -24.75 + 121 Reorder the terms: 121 + -22x + x2 = -24.75 + 121 Combine like terms: -24.75 + 121 = 96.25 121 + -22x + x2 = 96.25 Factor a perfect square on the left side: (x + -11)(x + -11) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + -11) equal to 9.810708435 and -9.810708435.Subproblem 1
x + -11 = 9.810708435 Simplifying x + -11 = 9.810708435 Reorder the terms: -11 + x = 9.810708435 Solving -11 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 9.810708435 + 11 Combine like terms: -11 + 11 = 0 0 + x = 9.810708435 + 11 x = 9.810708435 + 11 Combine like terms: 9.810708435 + 11 = 20.810708435 x = 20.810708435 Simplifying x = 20.810708435Subproblem 2
x + -11 = -9.810708435 Simplifying x + -11 = -9.810708435 Reorder the terms: -11 + x = -9.810708435 Solving -11 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -9.810708435 + 11 Combine like terms: -11 + 11 = 0 0 + x = -9.810708435 + 11 x = -9.810708435 + 11 Combine like terms: -9.810708435 + 11 = 1.189291565 x = 1.189291565 Simplifying x = 1.189291565Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.810708435, 1.189291565}Solution
x = {20.810708435, 1.189291565}
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