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Simplifying 10x2 + 11x + -34 = 0 Reorder the terms: -34 + 11x + 10x2 = 0 Solving -34 + 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'. -3.4 + 1.1x + x2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + 1.1x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + 1.1x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + 1.1x + x2 = 0 + 3.4 1.1x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 1.1x + x2 = 3.4 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 = 3.4 + 0.3025 Reorder the terms: 0.3025 + 1.1x + x2 = 3.4 + 0.3025 Combine like terms: 3.4 + 0.3025 = 3.7025 0.3025 + 1.1x + x2 = 3.7025 Factor a perfect square on the left side: (x + 0.55)(x + 0.55) = 3.7025 Calculate the square root of the right side: 1.92418814 Break this problem into two subproblems by setting (x + 0.55) equal to 1.92418814 and -1.92418814.Subproblem 1
x + 0.55 = 1.92418814 Simplifying x + 0.55 = 1.92418814 Reorder the terms: 0.55 + x = 1.92418814 Solving 0.55 + x = 1.92418814 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 = 1.92418814 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = 1.92418814 + -0.55 x = 1.92418814 + -0.55 Combine like terms: 1.92418814 + -0.55 = 1.37418814 x = 1.37418814 Simplifying x = 1.37418814Subproblem 2
x + 0.55 = -1.92418814 Simplifying x + 0.55 = -1.92418814 Reorder the terms: 0.55 + x = -1.92418814 Solving 0.55 + x = -1.92418814 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 = -1.92418814 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = -1.92418814 + -0.55 x = -1.92418814 + -0.55 Combine like terms: -1.92418814 + -0.55 = -2.47418814 x = -2.47418814 Simplifying x = -2.47418814Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.37418814, -2.47418814}
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