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Simplifying -16x2 + 207x + 20 = 0 Reorder the terms: 20 + 207x + -16x2 = 0 Solving 20 + 207x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1.25 + -12.9375x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -12.9375x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -12.9375x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -12.9375x + x2 = 0 + 1.25 -12.9375x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -12.9375x + x2 = 1.25 The x term is -12.9375x. Take half its coefficient (-6.46875). Square it (41.84472656) and add it to both sides. Add '41.84472656' to each side of the equation. -12.9375x + 41.84472656 + x2 = 1.25 + 41.84472656 Reorder the terms: 41.84472656 + -12.9375x + x2 = 1.25 + 41.84472656 Combine like terms: 1.25 + 41.84472656 = 43.09472656 41.84472656 + -12.9375x + x2 = 43.09472656 Factor a perfect square on the left side: (x + -6.46875)(x + -6.46875) = 43.09472656 Calculate the square root of the right side: 6.564657383 Break this problem into two subproblems by setting (x + -6.46875) equal to 6.564657383 and -6.564657383.Subproblem 1
x + -6.46875 = 6.564657383 Simplifying x + -6.46875 = 6.564657383 Reorder the terms: -6.46875 + x = 6.564657383 Solving -6.46875 + x = 6.564657383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.46875' to each side of the equation. -6.46875 + 6.46875 + x = 6.564657383 + 6.46875 Combine like terms: -6.46875 + 6.46875 = 0.00000 0.00000 + x = 6.564657383 + 6.46875 x = 6.564657383 + 6.46875 Combine like terms: 6.564657383 + 6.46875 = 13.033407383 x = 13.033407383 Simplifying x = 13.033407383Subproblem 2
x + -6.46875 = -6.564657383 Simplifying x + -6.46875 = -6.564657383 Reorder the terms: -6.46875 + x = -6.564657383 Solving -6.46875 + x = -6.564657383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.46875' to each side of the equation. -6.46875 + 6.46875 + x = -6.564657383 + 6.46875 Combine like terms: -6.46875 + 6.46875 = 0.00000 0.00000 + x = -6.564657383 + 6.46875 x = -6.564657383 + 6.46875 Combine like terms: -6.564657383 + 6.46875 = -0.095907383 x = -0.095907383 Simplifying x = -0.095907383Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.033407383, -0.095907383}
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