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Simplifying -16x2 + 24x + 125 = 0 Reorder the terms: 125 + 24x + -16x2 = 0 Solving 125 + 24x + -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'. -7.8125 + -1.5x + x2 = 0 Move the constant term to the right: Add '7.8125' to each side of the equation. -7.8125 + -1.5x + 7.8125 + x2 = 0 + 7.8125 Reorder the terms: -7.8125 + 7.8125 + -1.5x + x2 = 0 + 7.8125 Combine like terms: -7.8125 + 7.8125 = 0.0000 0.0000 + -1.5x + x2 = 0 + 7.8125 -1.5x + x2 = 0 + 7.8125 Combine like terms: 0 + 7.8125 = 7.8125 -1.5x + x2 = 7.8125 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 7.8125 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 7.8125 + 0.5625 Combine like terms: 7.8125 + 0.5625 = 8.375 0.5625 + -1.5x + x2 = 8.375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 8.375 Calculate the square root of the right side: 2.893959226 Break this problem into two subproblems by setting (x + -0.75) equal to 2.893959226 and -2.893959226.Subproblem 1
x + -0.75 = 2.893959226 Simplifying x + -0.75 = 2.893959226 Reorder the terms: -0.75 + x = 2.893959226 Solving -0.75 + x = 2.893959226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.893959226 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.893959226 + 0.75 x = 2.893959226 + 0.75 Combine like terms: 2.893959226 + 0.75 = 3.643959226 x = 3.643959226 Simplifying x = 3.643959226Subproblem 2
x + -0.75 = -2.893959226 Simplifying x + -0.75 = -2.893959226 Reorder the terms: -0.75 + x = -2.893959226 Solving -0.75 + x = -2.893959226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.893959226 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.893959226 + 0.75 x = -2.893959226 + 0.75 Combine like terms: -2.893959226 + 0.75 = -2.143959226 x = -2.143959226 Simplifying x = -2.143959226Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.643959226, -2.143959226}
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