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Simplifying 400 = x2 + 40x Reorder the terms: 400 = 40x + x2 Solving 400 = 40x + x2 Solving for variable 'x'. Reorder the terms: 400 + -40x + -1x2 = 40x + -40x + x2 + -1x2 Combine like terms: 40x + -40x = 0 400 + -40x + -1x2 = 0 + x2 + -1x2 400 + -40x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 400 + -40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -400 + 40x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + 40x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 40x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 40x + x2 = 0 + 400 40x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 40x + x2 = 400 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 400 + 400 Reorder the terms: 400 + 40x + x2 = 400 + 400 Combine like terms: 400 + 400 = 800 400 + 40x + x2 = 800 Factor a perfect square on the left side: (x + 20)(x + 20) = 800 Calculate the square root of the right side: 28.284271247 Break this problem into two subproblems by setting (x + 20) equal to 28.284271247 and -28.284271247.Subproblem 1
x + 20 = 28.284271247 Simplifying x + 20 = 28.284271247 Reorder the terms: 20 + x = 28.284271247 Solving 20 + x = 28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 28.284271247 + -20 Combine like terms: 20 + -20 = 0 0 + x = 28.284271247 + -20 x = 28.284271247 + -20 Combine like terms: 28.284271247 + -20 = 8.284271247 x = 8.284271247 Simplifying x = 8.284271247Subproblem 2
x + 20 = -28.284271247 Simplifying x + 20 = -28.284271247 Reorder the terms: 20 + x = -28.284271247 Solving 20 + x = -28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -28.284271247 + -20 Combine like terms: 20 + -20 = 0 0 + x = -28.284271247 + -20 x = -28.284271247 + -20 Combine like terms: -28.284271247 + -20 = -48.284271247 x = -48.284271247 Simplifying x = -48.284271247Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.284271247, -48.284271247}
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