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Simplifying 20x2 + 104x = 400 Reorder the terms: 104x + 20x2 = 400 Solving 104x + 20x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 104x + 20x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 104x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-100 + 26x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-100 + 26x + 5x2)' equal to zero and attempt to solve: Simplifying -100 + 26x + 5x2 = 0 Solving -100 + 26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -20 + 5.2x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 5.2x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 5.2x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 5.2x + x2 = 0 + 20 5.2x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 5.2x + x2 = 20 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = 20 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 20 + 6.76 Combine like terms: 20 + 6.76 = 26.76 6.76 + 5.2x + x2 = 26.76 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 26.76 Calculate the square root of the right side: 5.173006863 Break this problem into two subproblems by setting (x + 2.6) equal to 5.173006863 and -5.173006863.Subproblem 1
x + 2.6 = 5.173006863 Simplifying x + 2.6 = 5.173006863 Reorder the terms: 2.6 + x = 5.173006863 Solving 2.6 + x = 5.173006863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 5.173006863 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 5.173006863 + -2.6 x = 5.173006863 + -2.6 Combine like terms: 5.173006863 + -2.6 = 2.573006863 x = 2.573006863 Simplifying x = 2.573006863Subproblem 2
x + 2.6 = -5.173006863 Simplifying x + 2.6 = -5.173006863 Reorder the terms: 2.6 + x = -5.173006863 Solving 2.6 + x = -5.173006863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -5.173006863 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -5.173006863 + -2.6 x = -5.173006863 + -2.6 Combine like terms: -5.173006863 + -2.6 = -7.773006863 x = -7.773006863 Simplifying x = -7.773006863Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.573006863, -7.773006863}Solution
x = {2.573006863, -7.773006863}
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