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Simplifying 164 + -4x2 + -63x = 0 Reorder the terms: 164 + -63x + -4x2 = 0 Solving 164 + -63x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -41 + 15.75x + x2 = 0 Move the constant term to the right: Add '41' to each side of the equation. -41 + 15.75x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + 15.75x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 15.75x + x2 = 0 + 41 15.75x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 15.75x + x2 = 41 The x term is 15.75x. Take half its coefficient (7.875). Square it (62.015625) and add it to both sides. Add '62.015625' to each side of the equation. 15.75x + 62.015625 + x2 = 41 + 62.015625 Reorder the terms: 62.015625 + 15.75x + x2 = 41 + 62.015625 Combine like terms: 41 + 62.015625 = 103.015625 62.015625 + 15.75x + x2 = 103.015625 Factor a perfect square on the left side: (x + 7.875)(x + 7.875) = 103.015625 Calculate the square root of the right side: 10.149661324 Break this problem into two subproblems by setting (x + 7.875) equal to 10.149661324 and -10.149661324.Subproblem 1
x + 7.875 = 10.149661324 Simplifying x + 7.875 = 10.149661324 Reorder the terms: 7.875 + x = 10.149661324 Solving 7.875 + x = 10.149661324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.875' to each side of the equation. 7.875 + -7.875 + x = 10.149661324 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + x = 10.149661324 + -7.875 x = 10.149661324 + -7.875 Combine like terms: 10.149661324 + -7.875 = 2.274661324 x = 2.274661324 Simplifying x = 2.274661324Subproblem 2
x + 7.875 = -10.149661324 Simplifying x + 7.875 = -10.149661324 Reorder the terms: 7.875 + x = -10.149661324 Solving 7.875 + x = -10.149661324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.875' to each side of the equation. 7.875 + -7.875 + x = -10.149661324 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + x = -10.149661324 + -7.875 x = -10.149661324 + -7.875 Combine like terms: -10.149661324 + -7.875 = -18.024661324 x = -18.024661324 Simplifying x = -18.024661324Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.274661324, -18.024661324}
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