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Simplifying 5x(4x + 10) * 80 = 360 Reorder the terms: 5x(10 + 4x) * 80 = 360 Reorder the terms for easier multiplication: 5 * 80x(10 + 4x) = 360 Multiply 5 * 80 400x(10 + 4x) = 360 (10 * 400x + 4x * 400x) = 360 (4000x + 1600x2) = 360 Solving 4000x + 1600x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 4000x + 1600x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 4000x + 1600x2 = 0 Factor out the Greatest Common Factor (GCF), '40'. 40(-9 + 100x + 40x2) = 0 Ignore the factor 40.Subproblem 1
Set the factor '(-9 + 100x + 40x2)' equal to zero and attempt to solve: Simplifying -9 + 100x + 40x2 = 0 Solving -9 + 100x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.225 + 2.5x + x2 = 0.0 Move the constant term to the right: Add '0.225' to each side of the equation. -0.225 + 2.5x + 0.225 + x2 = 0.0 + 0.225 Reorder the terms: -0.225 + 0.225 + 2.5x + x2 = 0.0 + 0.225 Combine like terms: -0.225 + 0.225 = 0.000 0.000 + 2.5x + x2 = 0.0 + 0.225 2.5x + x2 = 0.0 + 0.225 Combine like terms: 0.0 + 0.225 = 0.225 2.5x + x2 = 0.225 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 = 0.225 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 0.225 + 1.5625 Combine like terms: 0.225 + 1.5625 = 1.7875 1.5625 + 2.5x + x2 = 1.7875 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 1.7875 Calculate the square root of the right side: 1.336974196 Break this problem into two subproblems by setting (x + 1.25) equal to 1.336974196 and -1.336974196.Subproblem 1
x + 1.25 = 1.336974196 Simplifying x + 1.25 = 1.336974196 Reorder the terms: 1.25 + x = 1.336974196 Solving 1.25 + x = 1.336974196 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 = 1.336974196 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.336974196 + -1.25 x = 1.336974196 + -1.25 Combine like terms: 1.336974196 + -1.25 = 0.086974196 x = 0.086974196 Simplifying x = 0.086974196Subproblem 2
x + 1.25 = -1.336974196 Simplifying x + 1.25 = -1.336974196 Reorder the terms: 1.25 + x = -1.336974196 Solving 1.25 + x = -1.336974196 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 = -1.336974196 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.336974196 + -1.25 x = -1.336974196 + -1.25 Combine like terms: -1.336974196 + -1.25 = -2.586974196 x = -2.586974196 Simplifying x = -2.586974196Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.086974196, -2.586974196}Solution
x = {0.086974196, -2.586974196}
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