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Simplifying 176 = -6.2x2 + 84.4x + -102.5 Reorder the terms: 176 = -102.5 + 84.4x + -6.2x2 Solving 176 = -102.5 + 84.4x + -6.2x2 Solving for variable 'x'. Combine like terms: 176 + 102.5 = 278.5 278.5 + -84.4x + 6.2x2 = -102.5 + 84.4x + -6.2x2 + 102.5 + -84.4x + 6.2x2 Reorder the terms: 278.5 + -84.4x + 6.2x2 = -102.5 + 102.5 + 84.4x + -84.4x + -6.2x2 + 6.2x2 Combine like terms: -102.5 + 102.5 = 0.0 278.5 + -84.4x + 6.2x2 = 0.0 + 84.4x + -84.4x + -6.2x2 + 6.2x2 278.5 + -84.4x + 6.2x2 = 84.4x + -84.4x + -6.2x2 + 6.2x2 Combine like terms: 84.4x + -84.4x = 0.0 278.5 + -84.4x + 6.2x2 = 0.0 + -6.2x2 + 6.2x2 278.5 + -84.4x + 6.2x2 = -6.2x2 + 6.2x2 Combine like terms: -6.2x2 + 6.2x2 = 0.0 278.5 + -84.4x + 6.2x2 = 0.0 Begin completing the square. Divide all terms by 6.2 the coefficient of the squared term: Divide each side by '6.2'. 44.91935484 + -13.61290323x + x2 = 0 Move the constant term to the right: Add '-44.91935484' to each side of the equation. 44.91935484 + -13.61290323x + -44.91935484 + x2 = 0 + -44.91935484 Reorder the terms: 44.91935484 + -44.91935484 + -13.61290323x + x2 = 0 + -44.91935484 Combine like terms: 44.91935484 + -44.91935484 = 0.00000000 0.00000000 + -13.61290323x + x2 = 0 + -44.91935484 -13.61290323x + x2 = 0 + -44.91935484 Combine like terms: 0 + -44.91935484 = -44.91935484 -13.61290323x + x2 = -44.91935484 The x term is -13.61290323x. Take half its coefficient (-6.806451615). Square it (46.32778359) and add it to both sides. Add '46.32778359' to each side of the equation. -13.61290323x + 46.32778359 + x2 = -44.91935484 + 46.32778359 Reorder the terms: 46.32778359 + -13.61290323x + x2 = -44.91935484 + 46.32778359 Combine like terms: -44.91935484 + 46.32778359 = 1.40842875 46.32778359 + -13.61290323x + x2 = 1.40842875 Factor a perfect square on the left side: (x + -6.806451615)(x + -6.806451615) = 1.40842875 Calculate the square root of the right side: 1.186772409 Break this problem into two subproblems by setting (x + -6.806451615) equal to 1.186772409 and -1.186772409.Subproblem 1
x + -6.806451615 = 1.186772409 Simplifying x + -6.806451615 = 1.186772409 Reorder the terms: -6.806451615 + x = 1.186772409 Solving -6.806451615 + x = 1.186772409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.806451615' to each side of the equation. -6.806451615 + 6.806451615 + x = 1.186772409 + 6.806451615 Combine like terms: -6.806451615 + 6.806451615 = 0.000000000 0.000000000 + x = 1.186772409 + 6.806451615 x = 1.186772409 + 6.806451615 Combine like terms: 1.186772409 + 6.806451615 = 7.993224024 x = 7.993224024 Simplifying x = 7.993224024Subproblem 2
x + -6.806451615 = -1.186772409 Simplifying x + -6.806451615 = -1.186772409 Reorder the terms: -6.806451615 + x = -1.186772409 Solving -6.806451615 + x = -1.186772409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.806451615' to each side of the equation. -6.806451615 + 6.806451615 + x = -1.186772409 + 6.806451615 Combine like terms: -6.806451615 + 6.806451615 = 0.000000000 0.000000000 + x = -1.186772409 + 6.806451615 x = -1.186772409 + 6.806451615 Combine like terms: -1.186772409 + 6.806451615 = 5.619679206 x = 5.619679206 Simplifying x = 5.619679206Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.993224024, 5.619679206}
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