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Simplifying 10x2 + 19x + -11 = 5.333 Reorder the terms: -11 + 19x + 10x2 = 5.333 Solving -11 + 19x + 10x2 = 5.333 Solving for variable 'x'. Reorder the terms: -11 + -5.333 + 19x + 10x2 = 5.333 + -5.333 Combine like terms: -11 + -5.333 = -16.333 -16.333 + 19x + 10x2 = 5.333 + -5.333 Combine like terms: 5.333 + -5.333 = 0.000 -16.333 + 19x + 10x2 = 0.000 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.6333 + 1.9x + x2 = 0.000 Move the constant term to the right: Add '1.6333' to each side of the equation. -1.6333 + 1.9x + 1.6333 + x2 = 0.000 + 1.6333 Reorder the terms: -1.6333 + 1.6333 + 1.9x + x2 = 0.000 + 1.6333 Combine like terms: -1.6333 + 1.6333 = 0.0000 0.0000 + 1.9x + x2 = 0.000 + 1.6333 1.9x + x2 = 0.000 + 1.6333 Combine like terms: 0.000 + 1.6333 = 1.6333 1.9x + x2 = 1.6333 The x term is 1.9x. Take half its coefficient (0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. 1.9x + 0.9025 + x2 = 1.6333 + 0.9025 Reorder the terms: 0.9025 + 1.9x + x2 = 1.6333 + 0.9025 Combine like terms: 1.6333 + 0.9025 = 2.5358 0.9025 + 1.9x + x2 = 2.5358 Factor a perfect square on the left side: (x + 0.95)(x + 0.95) = 2.5358 Calculate the square root of the right side: 1.592419543 Break this problem into two subproblems by setting (x + 0.95) equal to 1.592419543 and -1.592419543.Subproblem 1
x + 0.95 = 1.592419543 Simplifying x + 0.95 = 1.592419543 Reorder the terms: 0.95 + x = 1.592419543 Solving 0.95 + x = 1.592419543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = 1.592419543 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = 1.592419543 + -0.95 x = 1.592419543 + -0.95 Combine like terms: 1.592419543 + -0.95 = 0.642419543 x = 0.642419543 Simplifying x = 0.642419543Subproblem 2
x + 0.95 = -1.592419543 Simplifying x + 0.95 = -1.592419543 Reorder the terms: 0.95 + x = -1.592419543 Solving 0.95 + x = -1.592419543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = -1.592419543 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = -1.592419543 + -0.95 x = -1.592419543 + -0.95 Combine like terms: -1.592419543 + -0.95 = -2.542419543 x = -2.542419543 Simplifying x = -2.542419543Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.642419543, -2.542419543}
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