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Simplifying 10000 = (x2 + 100x) + -1(240x + 500) Reorder the terms: 10000 = (100x + x2) + -1(240x + 500) Remove parenthesis around (100x + x2) 10000 = 100x + x2 + -1(240x + 500) Reorder the terms: 10000 = 100x + x2 + -1(500 + 240x) 10000 = 100x + x2 + (500 * -1 + 240x * -1) 10000 = 100x + x2 + (-500 + -240x) Reorder the terms: 10000 = -500 + 100x + -240x + x2 Combine like terms: 100x + -240x = -140x 10000 = -500 + -140x + x2 Solving 10000 = -500 + -140x + x2 Solving for variable 'x'. Combine like terms: 10000 + 500 = 10500 10500 + 140x + -1x2 = -500 + -140x + x2 + 500 + 140x + -1x2 Reorder the terms: 10500 + 140x + -1x2 = -500 + 500 + -140x + 140x + x2 + -1x2 Combine like terms: -500 + 500 = 0 10500 + 140x + -1x2 = 0 + -140x + 140x + x2 + -1x2 10500 + 140x + -1x2 = -140x + 140x + x2 + -1x2 Combine like terms: -140x + 140x = 0 10500 + 140x + -1x2 = 0 + x2 + -1x2 10500 + 140x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10500 + 140x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10500 + -140x + x2 = 0 Move the constant term to the right: Add '10500' to each side of the equation. -10500 + -140x + 10500 + x2 = 0 + 10500 Reorder the terms: -10500 + 10500 + -140x + x2 = 0 + 10500 Combine like terms: -10500 + 10500 = 0 0 + -140x + x2 = 0 + 10500 -140x + x2 = 0 + 10500 Combine like terms: 0 + 10500 = 10500 -140x + x2 = 10500 The x term is -140x. Take half its coefficient (-70). Square it (4900) and add it to both sides. Add '4900' to each side of the equation. -140x + 4900 + x2 = 10500 + 4900 Reorder the terms: 4900 + -140x + x2 = 10500 + 4900 Combine like terms: 10500 + 4900 = 15400 4900 + -140x + x2 = 15400 Factor a perfect square on the left side: (x + -70)(x + -70) = 15400 Calculate the square root of the right side: 124.09673646 Break this problem into two subproblems by setting (x + -70) equal to 124.09673646 and -124.09673646.Subproblem 1
x + -70 = 124.09673646 Simplifying x + -70 = 124.09673646 Reorder the terms: -70 + x = 124.09673646 Solving -70 + x = 124.09673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = 124.09673646 + 70 Combine like terms: -70 + 70 = 0 0 + x = 124.09673646 + 70 x = 124.09673646 + 70 Combine like terms: 124.09673646 + 70 = 194.09673646 x = 194.09673646 Simplifying x = 194.09673646Subproblem 2
x + -70 = -124.09673646 Simplifying x + -70 = -124.09673646 Reorder the terms: -70 + x = -124.09673646 Solving -70 + x = -124.09673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = -124.09673646 + 70 Combine like terms: -70 + 70 = 0 0 + x = -124.09673646 + 70 x = -124.09673646 + 70 Combine like terms: -124.09673646 + 70 = -54.09673646 x = -54.09673646 Simplifying x = -54.09673646Solution
The solution to the problem is based on the solutions from the subproblems. x = {194.09673646, -54.09673646}
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