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Simplifying 25 + -8x2 + 8x = 0 Reorder the terms: 25 + 8x + -8x2 = 0 Solving 25 + 8x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + -1x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -1x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -1x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -1x + x2 = 0 + 3.125 -1x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -1x + x2 = 3.125 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 3.125 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3.125 + 0.25 Combine like terms: 3.125 + 0.25 = 3.375 0.25 + -1x + x2 = 3.375 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.375 Calculate the square root of the right side: 1.837117307 Break this problem into two subproblems by setting (x + -0.5) equal to 1.837117307 and -1.837117307.Subproblem 1
x + -0.5 = 1.837117307 Simplifying x + -0.5 = 1.837117307 Reorder the terms: -0.5 + x = 1.837117307 Solving -0.5 + x = 1.837117307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.837117307 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.837117307 + 0.5 x = 1.837117307 + 0.5 Combine like terms: 1.837117307 + 0.5 = 2.337117307 x = 2.337117307 Simplifying x = 2.337117307Subproblem 2
x + -0.5 = -1.837117307 Simplifying x + -0.5 = -1.837117307 Reorder the terms: -0.5 + x = -1.837117307 Solving -0.5 + x = -1.837117307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.837117307 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.837117307 + 0.5 x = -1.837117307 + 0.5 Combine like terms: -1.837117307 + 0.5 = -1.337117307 x = -1.337117307 Simplifying x = -1.337117307Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.337117307, -1.337117307}
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