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Simplifying 10x2 + -29x + -22 = 0 Reorder the terms: -22 + -29x + 10x2 = 0 Solving -22 + -29x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.2 + -2.9x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -2.9x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -2.9x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -2.9x + x2 = 0 + 2.2 -2.9x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -2.9x + x2 = 2.2 The x term is -2.9x. Take half its coefficient (-1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. -2.9x + 2.1025 + x2 = 2.2 + 2.1025 Reorder the terms: 2.1025 + -2.9x + x2 = 2.2 + 2.1025 Combine like terms: 2.2 + 2.1025 = 4.3025 2.1025 + -2.9x + x2 = 4.3025 Factor a perfect square on the left side: (x + -1.45)(x + -1.45) = 4.3025 Calculate the square root of the right side: 2.074246851 Break this problem into two subproblems by setting (x + -1.45) equal to 2.074246851 and -2.074246851.Subproblem 1
x + -1.45 = 2.074246851 Simplifying x + -1.45 = 2.074246851 Reorder the terms: -1.45 + x = 2.074246851 Solving -1.45 + x = 2.074246851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = 2.074246851 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = 2.074246851 + 1.45 x = 2.074246851 + 1.45 Combine like terms: 2.074246851 + 1.45 = 3.524246851 x = 3.524246851 Simplifying x = 3.524246851Subproblem 2
x + -1.45 = -2.074246851 Simplifying x + -1.45 = -2.074246851 Reorder the terms: -1.45 + x = -2.074246851 Solving -1.45 + x = -2.074246851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = -2.074246851 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = -2.074246851 + 1.45 x = -2.074246851 + 1.45 Combine like terms: -2.074246851 + 1.45 = -0.624246851 x = -0.624246851 Simplifying x = -0.624246851Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.524246851, -0.624246851}
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