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Simplifying x2 + 2x + 400 = 3x2 + -50x + 100 Reorder the terms: 400 + 2x + x2 = 3x2 + -50x + 100 Reorder the terms: 400 + 2x + x2 = 100 + -50x + 3x2 Solving 400 + 2x + x2 = 100 + -50x + 3x2 Solving for variable 'x'. Reorder the terms: 400 + -100 + 2x + 50x + x2 + -3x2 = 100 + -50x + 3x2 + -100 + 50x + -3x2 Combine like terms: 400 + -100 = 300 300 + 2x + 50x + x2 + -3x2 = 100 + -50x + 3x2 + -100 + 50x + -3x2 Combine like terms: 2x + 50x = 52x 300 + 52x + x2 + -3x2 = 100 + -50x + 3x2 + -100 + 50x + -3x2 Combine like terms: x2 + -3x2 = -2x2 300 + 52x + -2x2 = 100 + -50x + 3x2 + -100 + 50x + -3x2 Reorder the terms: 300 + 52x + -2x2 = 100 + -100 + -50x + 50x + 3x2 + -3x2 Combine like terms: 100 + -100 = 0 300 + 52x + -2x2 = 0 + -50x + 50x + 3x2 + -3x2 300 + 52x + -2x2 = -50x + 50x + 3x2 + -3x2 Combine like terms: -50x + 50x = 0 300 + 52x + -2x2 = 0 + 3x2 + -3x2 300 + 52x + -2x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 300 + 52x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(150 + 26x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(150 + 26x + -1x2)' equal to zero and attempt to solve: Simplifying 150 + 26x + -1x2 = 0 Solving 150 + 26x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -150 + -26x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + -26x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + -26x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -26x + x2 = 0 + 150 -26x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 -26x + x2 = 150 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = 150 + 169 Reorder the terms: 169 + -26x + x2 = 150 + 169 Combine like terms: 150 + 169 = 319 169 + -26x + x2 = 319 Factor a perfect square on the left side: (x + -13)(x + -13) = 319 Calculate the square root of the right side: 17.860571099 Break this problem into two subproblems by setting (x + -13) equal to 17.860571099 and -17.860571099.Subproblem 1
x + -13 = 17.860571099 Simplifying x + -13 = 17.860571099 Reorder the terms: -13 + x = 17.860571099 Solving -13 + x = 17.860571099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 17.860571099 + 13 Combine like terms: -13 + 13 = 0 0 + x = 17.860571099 + 13 x = 17.860571099 + 13 Combine like terms: 17.860571099 + 13 = 30.860571099 x = 30.860571099 Simplifying x = 30.860571099Subproblem 2
x + -13 = -17.860571099 Simplifying x + -13 = -17.860571099 Reorder the terms: -13 + x = -17.860571099 Solving -13 + x = -17.860571099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -17.860571099 + 13 Combine like terms: -13 + 13 = 0 0 + x = -17.860571099 + 13 x = -17.860571099 + 13 Combine like terms: -17.860571099 + 13 = -4.860571099 x = -4.860571099 Simplifying x = -4.860571099Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.860571099, -4.860571099}Solution
x = {30.860571099, -4.860571099}
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