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Simplifying -16x2 + -40x + 25 = 0 Reorder the terms: 25 + -40x + -16x2 = 0 Solving 25 + -40x + -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'. -1.5625 + 2.5x + x2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 2.5x + 1.5625 + x2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 2.5x + x2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 2.5x + x2 = 0 + 1.5625 2.5x + x2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 2.5x + x2 = 1.5625 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 1.5625 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 1.5625 + 1.5625 Combine like terms: 1.5625 + 1.5625 = 3.125 1.5625 + 2.5x + x2 = 3.125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (x + 1.25) equal to 1.767766953 and -1.767766953.Subproblem 1
x + 1.25 = 1.767766953 Simplifying x + 1.25 = 1.767766953 Reorder the terms: 1.25 + x = 1.767766953 Solving 1.25 + x = 1.767766953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.767766953 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.767766953 + -1.25 x = 1.767766953 + -1.25 Combine like terms: 1.767766953 + -1.25 = 0.517766953 x = 0.517766953 Simplifying x = 0.517766953Subproblem 2
x + 1.25 = -1.767766953 Simplifying x + 1.25 = -1.767766953 Reorder the terms: 1.25 + x = -1.767766953 Solving 1.25 + x = -1.767766953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.767766953 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.767766953 + -1.25 x = -1.767766953 + -1.25 Combine like terms: -1.767766953 + -1.25 = -3.017766953 x = -3.017766953 Simplifying x = -3.017766953Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.517766953, -3.017766953}
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