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Simplifying 124x2 + -210 = 25x Reorder the terms: -210 + 124x2 = 25x Solving -210 + 124x2 = 25x Solving for variable 'x'. Reorder the terms: -210 + -25x + 124x2 = 25x + -25x Combine like terms: 25x + -25x = 0 -210 + -25x + 124x2 = 0 Begin completing the square. Divide all terms by 124 the coefficient of the squared term: Divide each side by '124'. -1.693548387 + -0.2016129032x + x2 = 0 Move the constant term to the right: Add '1.693548387' to each side of the equation. -1.693548387 + -0.2016129032x + 1.693548387 + x2 = 0 + 1.693548387 Reorder the terms: -1.693548387 + 1.693548387 + -0.2016129032x + x2 = 0 + 1.693548387 Combine like terms: -1.693548387 + 1.693548387 = 0.000000000 0.000000000 + -0.2016129032x + x2 = 0 + 1.693548387 -0.2016129032x + x2 = 0 + 1.693548387 Combine like terms: 0 + 1.693548387 = 1.693548387 -0.2016129032x + x2 = 1.693548387 The x term is -0.2016129032x. Take half its coefficient (-0.1008064516). Square it (0.01016194068) and add it to both sides. Add '0.01016194068' to each side of the equation. -0.2016129032x + 0.01016194068 + x2 = 1.693548387 + 0.01016194068 Reorder the terms: 0.01016194068 + -0.2016129032x + x2 = 1.693548387 + 0.01016194068 Combine like terms: 1.693548387 + 0.01016194068 = 1.70371032768 0.01016194068 + -0.2016129032x + x2 = 1.70371032768 Factor a perfect square on the left side: (x + -0.1008064516)(x + -0.1008064516) = 1.70371032768 Calculate the square root of the right side: 1.305262551 Break this problem into two subproblems by setting (x + -0.1008064516) equal to 1.305262551 and -1.305262551.Subproblem 1
x + -0.1008064516 = 1.305262551 Simplifying x + -0.1008064516 = 1.305262551 Reorder the terms: -0.1008064516 + x = 1.305262551 Solving -0.1008064516 + x = 1.305262551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1008064516' to each side of the equation. -0.1008064516 + 0.1008064516 + x = 1.305262551 + 0.1008064516 Combine like terms: -0.1008064516 + 0.1008064516 = 0.0000000000 0.0000000000 + x = 1.305262551 + 0.1008064516 x = 1.305262551 + 0.1008064516 Combine like terms: 1.305262551 + 0.1008064516 = 1.4060690026 x = 1.4060690026 Simplifying x = 1.4060690026Subproblem 2
x + -0.1008064516 = -1.305262551 Simplifying x + -0.1008064516 = -1.305262551 Reorder the terms: -0.1008064516 + x = -1.305262551 Solving -0.1008064516 + x = -1.305262551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1008064516' to each side of the equation. -0.1008064516 + 0.1008064516 + x = -1.305262551 + 0.1008064516 Combine like terms: -0.1008064516 + 0.1008064516 = 0.0000000000 0.0000000000 + x = -1.305262551 + 0.1008064516 x = -1.305262551 + 0.1008064516 Combine like terms: -1.305262551 + 0.1008064516 = -1.2044560994 x = -1.2044560994 Simplifying x = -1.2044560994Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4060690026, -1.2044560994}
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