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Simplifying 10x2 + -9 + 5x + -8x2 + -11 = 0 Reorder the terms: -9 + -11 + 5x + 10x2 + -8x2 = 0 Combine like terms: -9 + -11 = -20 -20 + 5x + 10x2 + -8x2 = 0 Combine like terms: 10x2 + -8x2 = 2x2 -20 + 5x + 2x2 = 0 Solving -20 + 5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + 2.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 2.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 2.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2.5x + x2 = 0 + 10 2.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 2.5x + x2 = 10 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 = 10 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 10 + 1.5625 Combine like terms: 10 + 1.5625 = 11.5625 1.5625 + 2.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + 1.25) equal to 3.400367627 and -3.400367627.Subproblem 1
x + 1.25 = 3.400367627 Simplifying x + 1.25 = 3.400367627 Reorder the terms: 1.25 + x = 3.400367627 Solving 1.25 + x = 3.400367627 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 = 3.400367627 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.400367627 + -1.25 x = 3.400367627 + -1.25 Combine like terms: 3.400367627 + -1.25 = 2.150367627 x = 2.150367627 Simplifying x = 2.150367627Subproblem 2
x + 1.25 = -3.400367627 Simplifying x + 1.25 = -3.400367627 Reorder the terms: 1.25 + x = -3.400367627 Solving 1.25 + x = -3.400367627 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 = -3.400367627 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.400367627 + -1.25 x = -3.400367627 + -1.25 Combine like terms: -3.400367627 + -1.25 = -4.650367627 x = -4.650367627 Simplifying x = -4.650367627Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.150367627, -4.650367627}
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