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Simplifying 10x2 + 11x + -28 = 0 Reorder the terms: -28 + 11x + 10x2 = 0 Solving -28 + 11x + 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'. -2.8 + 1.1x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 1.1x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 1.1x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 1.1x + x2 = 0 + 2.8 1.1x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 1.1x + x2 = 2.8 The x term is 1.1x. Take half its coefficient (0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. 1.1x + 0.3025 + x2 = 2.8 + 0.3025 Reorder the terms: 0.3025 + 1.1x + x2 = 2.8 + 0.3025 Combine like terms: 2.8 + 0.3025 = 3.1025 0.3025 + 1.1x + x2 = 3.1025 Factor a perfect square on the left side: (x + 0.55)(x + 0.55) = 3.1025 Calculate the square root of the right side: 1.761391495 Break this problem into two subproblems by setting (x + 0.55) equal to 1.761391495 and -1.761391495.Subproblem 1
x + 0.55 = 1.761391495 Simplifying x + 0.55 = 1.761391495 Reorder the terms: 0.55 + x = 1.761391495 Solving 0.55 + x = 1.761391495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = 1.761391495 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = 1.761391495 + -0.55 x = 1.761391495 + -0.55 Combine like terms: 1.761391495 + -0.55 = 1.211391495 x = 1.211391495 Simplifying x = 1.211391495Subproblem 2
x + 0.55 = -1.761391495 Simplifying x + 0.55 = -1.761391495 Reorder the terms: 0.55 + x = -1.761391495 Solving 0.55 + x = -1.761391495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = -1.761391495 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = -1.761391495 + -0.55 x = -1.761391495 + -0.55 Combine like terms: -1.761391495 + -0.55 = -2.311391495 x = -2.311391495 Simplifying x = -2.311391495Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.211391495, -2.311391495}
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