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Simplifying -16x2 + 24x + 9 = 0 Reorder the terms: 9 + 24x + -16x2 = 0 Solving 9 + 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'. -0.5625 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -1.5x + 0.5625 + x2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -1.5x + x2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -1.5x + x2 = 0 + 0.5625 -1.5x + x2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -1.5x + x2 = 0.5625 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 = 0.5625 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.5625 + 0.5625 Combine like terms: 0.5625 + 0.5625 = 1.125 0.5625 + -1.5x + x2 = 1.125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.125 Calculate the square root of the right side: 1.060660172 Break this problem into two subproblems by setting (x + -0.75) equal to 1.060660172 and -1.060660172.Subproblem 1
x + -0.75 = 1.060660172 Simplifying x + -0.75 = 1.060660172 Reorder the terms: -0.75 + x = 1.060660172 Solving -0.75 + x = 1.060660172 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 = 1.060660172 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.060660172 + 0.75 x = 1.060660172 + 0.75 Combine like terms: 1.060660172 + 0.75 = 1.810660172 x = 1.810660172 Simplifying x = 1.810660172Subproblem 2
x + -0.75 = -1.060660172 Simplifying x + -0.75 = -1.060660172 Reorder the terms: -0.75 + x = -1.060660172 Solving -0.75 + x = -1.060660172 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 = -1.060660172 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.060660172 + 0.75 x = -1.060660172 + 0.75 Combine like terms: -1.060660172 + 0.75 = -0.310660172 x = -0.310660172 Simplifying x = -0.310660172Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.810660172, -0.310660172}
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