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Simplifying -5x2 + 100x + -250 = 100 Reorder the terms: -250 + 100x + -5x2 = 100 Solving -250 + 100x + -5x2 = 100 Solving for variable 'x'. Reorder the terms: -250 + -100 + 100x + -5x2 = 100 + -100 Combine like terms: -250 + -100 = -350 -350 + 100x + -5x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -350 + 100x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-70 + 20x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-70 + 20x + -1x2)' equal to zero and attempt to solve: Simplifying -70 + 20x + -1x2 = 0 Solving -70 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 70 + -20x + x2 = 0 Move the constant term to the right: Add '-70' to each side of the equation. 70 + -20x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + -20x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -20x + x2 = 0 + -70 -20x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 -20x + x2 = -70 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 = -70 + 100 Reorder the terms: 100 + -20x + x2 = -70 + 100 Combine like terms: -70 + 100 = 30 100 + -20x + x2 = 30 Factor a perfect square on the left side: (x + -10)(x + -10) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + -10) equal to 5.477225575 and -5.477225575.Subproblem 1
x + -10 = 5.477225575 Simplifying x + -10 = 5.477225575 Reorder the terms: -10 + x = 5.477225575 Solving -10 + x = 5.477225575 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 = 5.477225575 + 10 Combine like terms: -10 + 10 = 0 0 + x = 5.477225575 + 10 x = 5.477225575 + 10 Combine like terms: 5.477225575 + 10 = 15.477225575 x = 15.477225575 Simplifying x = 15.477225575Subproblem 2
x + -10 = -5.477225575 Simplifying x + -10 = -5.477225575 Reorder the terms: -10 + x = -5.477225575 Solving -10 + x = -5.477225575 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 = -5.477225575 + 10 Combine like terms: -10 + 10 = 0 0 + x = -5.477225575 + 10 x = -5.477225575 + 10 Combine like terms: -5.477225575 + 10 = 4.522774425 x = 4.522774425 Simplifying x = 4.522774425Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.477225575, 4.522774425}Solution
x = {15.477225575, 4.522774425}
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