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Simplifying 9x2 + -13x = 40 Reorder the terms: -13x + 9x2 = 40 Solving -13x + 9x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + -13x + 9x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -13x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4.444444444 + -1.444444444x + x2 = 0 Move the constant term to the right: Add '4.444444444' to each side of the equation. -4.444444444 + -1.444444444x + 4.444444444 + x2 = 0 + 4.444444444 Reorder the terms: -4.444444444 + 4.444444444 + -1.444444444x + x2 = 0 + 4.444444444 Combine like terms: -4.444444444 + 4.444444444 = 0.000000000 0.000000000 + -1.444444444x + x2 = 0 + 4.444444444 -1.444444444x + x2 = 0 + 4.444444444 Combine like terms: 0 + 4.444444444 = 4.444444444 -1.444444444x + x2 = 4.444444444 The x term is -1.444444444x. Take half its coefficient (-0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. -1.444444444x + 0.5216049380 + x2 = 4.444444444 + 0.5216049380 Reorder the terms: 0.5216049380 + -1.444444444x + x2 = 4.444444444 + 0.5216049380 Combine like terms: 4.444444444 + 0.5216049380 = 4.966049382 0.5216049380 + -1.444444444x + x2 = 4.966049382 Factor a perfect square on the left side: (x + -0.722222222)(x + -0.722222222) = 4.966049382 Calculate the square root of the right side: 2.228463458 Break this problem into two subproblems by setting (x + -0.722222222) equal to 2.228463458 and -2.228463458.Subproblem 1
x + -0.722222222 = 2.228463458 Simplifying x + -0.722222222 = 2.228463458 Reorder the terms: -0.722222222 + x = 2.228463458 Solving -0.722222222 + x = 2.228463458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = 2.228463458 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = 2.228463458 + 0.722222222 x = 2.228463458 + 0.722222222 Combine like terms: 2.228463458 + 0.722222222 = 2.95068568 x = 2.95068568 Simplifying x = 2.95068568Subproblem 2
x + -0.722222222 = -2.228463458 Simplifying x + -0.722222222 = -2.228463458 Reorder the terms: -0.722222222 + x = -2.228463458 Solving -0.722222222 + x = -2.228463458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = -2.228463458 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = -2.228463458 + 0.722222222 x = -2.228463458 + 0.722222222 Combine like terms: -2.228463458 + 0.722222222 = -1.506241236 x = -1.506241236 Simplifying x = -1.506241236Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.95068568, -1.506241236}
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