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Simplifying 10x2 + 11x + -16 = 16 Reorder the terms: -16 + 11x + 10x2 = 16 Solving -16 + 11x + 10x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + -16 + 11x + 10x2 = 16 + -16 Combine like terms: -16 + -16 = -32 -32 + 11x + 10x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -32 + 11x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3.2 + 1.1x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 1.1x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 1.1x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 1.1x + x2 = 0 + 3.2 1.1x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 1.1x + x2 = 3.2 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 = 3.2 + 0.3025 Reorder the terms: 0.3025 + 1.1x + x2 = 3.2 + 0.3025 Combine like terms: 3.2 + 0.3025 = 3.5025 0.3025 + 1.1x + x2 = 3.5025 Factor a perfect square on the left side: (x + 0.55)(x + 0.55) = 3.5025 Calculate the square root of the right side: 1.871496727 Break this problem into two subproblems by setting (x + 0.55) equal to 1.871496727 and -1.871496727.Subproblem 1
x + 0.55 = 1.871496727 Simplifying x + 0.55 = 1.871496727 Reorder the terms: 0.55 + x = 1.871496727 Solving 0.55 + x = 1.871496727 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 = 1.871496727 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = 1.871496727 + -0.55 x = 1.871496727 + -0.55 Combine like terms: 1.871496727 + -0.55 = 1.321496727 x = 1.321496727 Simplifying x = 1.321496727Subproblem 2
x + 0.55 = -1.871496727 Simplifying x + 0.55 = -1.871496727 Reorder the terms: 0.55 + x = -1.871496727 Solving 0.55 + x = -1.871496727 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 = -1.871496727 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = -1.871496727 + -0.55 x = -1.871496727 + -0.55 Combine like terms: -1.871496727 + -0.55 = -2.421496727 x = -2.421496727 Simplifying x = -2.421496727Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.321496727, -2.421496727}
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