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Simplifying -0.01x2 + 0.4x + 5.9 = 0 Reorder the terms: 5.9 + 0.4x + -0.01x2 = 0 Solving 5.9 + 0.4x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -590 + -40x + x2 = 0 Move the constant term to the right: Add '590' to each side of the equation. -590 + -40x + 590 + x2 = 0 + 590 Reorder the terms: -590 + 590 + -40x + x2 = 0 + 590 Combine like terms: -590 + 590 = 0 0 + -40x + x2 = 0 + 590 -40x + x2 = 0 + 590 Combine like terms: 0 + 590 = 590 -40x + x2 = 590 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 = 590 + 400 Reorder the terms: 400 + -40x + x2 = 590 + 400 Combine like terms: 590 + 400 = 990 400 + -40x + x2 = 990 Factor a perfect square on the left side: (x + -20)(x + -20) = 990 Calculate the square root of the right side: 31.464265445 Break this problem into two subproblems by setting (x + -20) equal to 31.464265445 and -31.464265445.Subproblem 1
x + -20 = 31.464265445 Simplifying x + -20 = 31.464265445 Reorder the terms: -20 + x = 31.464265445 Solving -20 + x = 31.464265445 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 = 31.464265445 + 20 Combine like terms: -20 + 20 = 0 0 + x = 31.464265445 + 20 x = 31.464265445 + 20 Combine like terms: 31.464265445 + 20 = 51.464265445 x = 51.464265445 Simplifying x = 51.464265445Subproblem 2
x + -20 = -31.464265445 Simplifying x + -20 = -31.464265445 Reorder the terms: -20 + x = -31.464265445 Solving -20 + x = -31.464265445 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 = -31.464265445 + 20 Combine like terms: -20 + 20 = 0 0 + x = -31.464265445 + 20 x = -31.464265445 + 20 Combine like terms: -31.464265445 + 20 = -11.464265445 x = -11.464265445 Simplifying x = -11.464265445Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.464265445, -11.464265445}
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