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Simplifying 80x2 + 120x = 45 Reorder the terms: 120x + 80x2 = 45 Solving 120x + 80x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 120x + 80x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 120x + 80x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + 24x + 16x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + 24x + 16x2)' equal to zero and attempt to solve: Simplifying -9 + 24x + 16x2 = 0 Solving -9 + 24x + 16x2 = 0 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 = 0.310660172 x = 0.310660172 Simplifying x = 0.310660172Subproblem 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 = -1.810660172 x = -1.810660172 Simplifying x = -1.810660172Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.310660172, -1.810660172}Solution
x = {0.310660172, -1.810660172}
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