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Simplifying 0 = 2x2 + -5x + -210 Reorder the terms: 0 = -210 + -5x + 2x2 Solving 0 = -210 + -5x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 210 = 210 210 + 5x + -2x2 = -210 + -5x + 2x2 + 210 + 5x + -2x2 Reorder the terms: 210 + 5x + -2x2 = -210 + 210 + -5x + 5x + 2x2 + -2x2 Combine like terms: -210 + 210 = 0 210 + 5x + -2x2 = 0 + -5x + 5x + 2x2 + -2x2 210 + 5x + -2x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 210 + 5x + -2x2 = 0 + 2x2 + -2x2 210 + 5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 210 + 5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -105 + -2.5x + x2 = 0 Move the constant term to the right: Add '105' to each side of the equation. -105 + -2.5x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + -2.5x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + -2.5x + x2 = 0 + 105 -2.5x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 -2.5x + x2 = 105 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 105 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 105 + 1.5625 Combine like terms: 105 + 1.5625 = 106.5625 1.5625 + -2.5x + x2 = 106.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 106.5625 Calculate the square root of the right side: 10.322911411 Break this problem into two subproblems by setting (x + -1.25) equal to 10.322911411 and -10.322911411.Subproblem 1
x + -1.25 = 10.322911411 Simplifying x + -1.25 = 10.322911411 Reorder the terms: -1.25 + x = 10.322911411 Solving -1.25 + x = 10.322911411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 10.322911411 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 10.322911411 + 1.25 x = 10.322911411 + 1.25 Combine like terms: 10.322911411 + 1.25 = 11.572911411 x = 11.572911411 Simplifying x = 11.572911411Subproblem 2
x + -1.25 = -10.322911411 Simplifying x + -1.25 = -10.322911411 Reorder the terms: -1.25 + x = -10.322911411 Solving -1.25 + x = -10.322911411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -10.322911411 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -10.322911411 + 1.25 x = -10.322911411 + 1.25 Combine like terms: -10.322911411 + 1.25 = -9.072911411 x = -9.072911411 Simplifying x = -9.072911411Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.572911411, -9.072911411}
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