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Simplifying 5(x + 80) + -4x(x + -20) = 5x Reorder the terms: 5(80 + x) + -4x(x + -20) = 5x (80 * 5 + x * 5) + -4x(x + -20) = 5x (400 + 5x) + -4x(x + -20) = 5x Reorder the terms: 400 + 5x + -4x(-20 + x) = 5x 400 + 5x + (-20 * -4x + x * -4x) = 5x 400 + 5x + (80x + -4x2) = 5x Combine like terms: 5x + 80x = 85x 400 + 85x + -4x2 = 5x Solving 400 + 85x + -4x2 = 5x Solving for variable 'x'. Reorder the terms: 400 + 85x + -5x + -4x2 = 5x + -5x Combine like terms: 85x + -5x = 80x 400 + 80x + -4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 400 + 80x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(100 + 20x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(100 + 20x + -1x2)' equal to zero and attempt to solve: Simplifying 100 + 20x + -1x2 = 0 Solving 100 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + -20x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -20x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -20x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -20x + x2 = 0 + 100 -20x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -20x + x2 = 100 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 100 + 100 Reorder the terms: 100 + -20x + x2 = 100 + 100 Combine like terms: 100 + 100 = 200 100 + -20x + x2 = 200 Factor a perfect square on the left side: (x + -10)(x + -10) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + -10) equal to 14.142135624 and -14.142135624.Subproblem 1
x + -10 = 14.142135624 Simplifying x + -10 = 14.142135624 Reorder the terms: -10 + x = 14.142135624 Solving -10 + x = 14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 14.142135624 + 10 Combine like terms: -10 + 10 = 0 0 + x = 14.142135624 + 10 x = 14.142135624 + 10 Combine like terms: 14.142135624 + 10 = 24.142135624 x = 24.142135624 Simplifying x = 24.142135624Subproblem 2
x + -10 = -14.142135624 Simplifying x + -10 = -14.142135624 Reorder the terms: -10 + x = -14.142135624 Solving -10 + x = -14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -14.142135624 + 10 Combine like terms: -10 + 10 = 0 0 + x = -14.142135624 + 10 x = -14.142135624 + 10 Combine like terms: -14.142135624 + 10 = -4.142135624 x = -4.142135624 Simplifying x = -4.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.142135624, -4.142135624}Solution
x = {24.142135624, -4.142135624}
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