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Simplifying 100x + -2x2 = 100 + x Solving 100x + -2x2 = 100 + x Solving for variable 'x'. Reorder the terms: -100 + 100x + -1x + -2x2 = 100 + x + -100 + -1x Combine like terms: 100x + -1x = 99x -100 + 99x + -2x2 = 100 + x + -100 + -1x Reorder the terms: -100 + 99x + -2x2 = 100 + -100 + x + -1x Combine like terms: 100 + -100 = 0 -100 + 99x + -2x2 = 0 + x + -1x -100 + 99x + -2x2 = x + -1x Combine like terms: x + -1x = 0 -100 + 99x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 50 + -49.5x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -49.5x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -49.5x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -49.5x + x2 = 0 + -50 -49.5x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -49.5x + x2 = -50 The x term is -49.5x. Take half its coefficient (-24.75). Square it (612.5625) and add it to both sides. Add '612.5625' to each side of the equation. -49.5x + 612.5625 + x2 = -50 + 612.5625 Reorder the terms: 612.5625 + -49.5x + x2 = -50 + 612.5625 Combine like terms: -50 + 612.5625 = 562.5625 612.5625 + -49.5x + x2 = 562.5625 Factor a perfect square on the left side: (x + -24.75)(x + -24.75) = 562.5625 Calculate the square root of the right side: 23.71840003 Break this problem into two subproblems by setting (x + -24.75) equal to 23.71840003 and -23.71840003.Subproblem 1
x + -24.75 = 23.71840003 Simplifying x + -24.75 = 23.71840003 Reorder the terms: -24.75 + x = 23.71840003 Solving -24.75 + x = 23.71840003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.75' to each side of the equation. -24.75 + 24.75 + x = 23.71840003 + 24.75 Combine like terms: -24.75 + 24.75 = 0.00 0.00 + x = 23.71840003 + 24.75 x = 23.71840003 + 24.75 Combine like terms: 23.71840003 + 24.75 = 48.46840003 x = 48.46840003 Simplifying x = 48.46840003Subproblem 2
x + -24.75 = -23.71840003 Simplifying x + -24.75 = -23.71840003 Reorder the terms: -24.75 + x = -23.71840003 Solving -24.75 + x = -23.71840003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.75' to each side of the equation. -24.75 + 24.75 + x = -23.71840003 + 24.75 Combine like terms: -24.75 + 24.75 = 0.00 0.00 + x = -23.71840003 + 24.75 x = -23.71840003 + 24.75 Combine like terms: -23.71840003 + 24.75 = 1.03159997 x = 1.03159997 Simplifying x = 1.03159997Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.46840003, 1.03159997}
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