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Simplifying 13 = x2 + -0.20x Reorder the terms: 13 = -0.20x + x2 Solving 13 = -0.20x + x2 Solving for variable 'x'. Reorder the terms: 13 + 0.20x + -1x2 = -0.20x + 0.20x + x2 + -1x2 Combine like terms: -0.20x + 0.20x = 0.00 13 + 0.20x + -1x2 = 0.00 + x2 + -1x2 13 + 0.20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 13 + 0.20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + -0.2x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -0.2x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -0.2x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -0.2x + x2 = 0 + 13 -0.2x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -0.2x + x2 = 13 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 13 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 13 + 0.01 Combine like terms: 13 + 0.01 = 13.01 0.01 + -0.2x + x2 = 13.01 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 13.01 Calculate the square root of the right side: 3.606937759 Break this problem into two subproblems by setting (x + -0.1) equal to 3.606937759 and -3.606937759.Subproblem 1
x + -0.1 = 3.606937759 Simplifying x + -0.1 = 3.606937759 Reorder the terms: -0.1 + x = 3.606937759 Solving -0.1 + x = 3.606937759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 3.606937759 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 3.606937759 + 0.1 x = 3.606937759 + 0.1 Combine like terms: 3.606937759 + 0.1 = 3.706937759 x = 3.706937759 Simplifying x = 3.706937759Subproblem 2
x + -0.1 = -3.606937759 Simplifying x + -0.1 = -3.606937759 Reorder the terms: -0.1 + x = -3.606937759 Solving -0.1 + x = -3.606937759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -3.606937759 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -3.606937759 + 0.1 x = -3.606937759 + 0.1 Combine like terms: -3.606937759 + 0.1 = -3.506937759 x = -3.506937759 Simplifying x = -3.506937759Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.706937759, -3.506937759}
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