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Simplifying 10x2 + -29x + -90 = 0 Reorder the terms: -90 + -29x + 10x2 = 0 Solving -90 + -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'. -9 + -2.9x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -2.9x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -2.9x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2.9x + x2 = 0 + 9 -2.9x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2.9x + x2 = 9 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 = 9 + 2.1025 Reorder the terms: 2.1025 + -2.9x + x2 = 9 + 2.1025 Combine like terms: 9 + 2.1025 = 11.1025 2.1025 + -2.9x + x2 = 11.1025 Factor a perfect square on the left side: (x + -1.45)(x + -1.45) = 11.1025 Calculate the square root of the right side: 3.332041416 Break this problem into two subproblems by setting (x + -1.45) equal to 3.332041416 and -3.332041416.Subproblem 1
x + -1.45 = 3.332041416 Simplifying x + -1.45 = 3.332041416 Reorder the terms: -1.45 + x = 3.332041416 Solving -1.45 + x = 3.332041416 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 = 3.332041416 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = 3.332041416 + 1.45 x = 3.332041416 + 1.45 Combine like terms: 3.332041416 + 1.45 = 4.782041416 x = 4.782041416 Simplifying x = 4.782041416Subproblem 2
x + -1.45 = -3.332041416 Simplifying x + -1.45 = -3.332041416 Reorder the terms: -1.45 + x = -3.332041416 Solving -1.45 + x = -3.332041416 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 = -3.332041416 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = -3.332041416 + 1.45 x = -3.332041416 + 1.45 Combine like terms: -3.332041416 + 1.45 = -1.882041416 x = -1.882041416 Simplifying x = -1.882041416Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.782041416, -1.882041416}
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