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Simplifying 10x2 + 39x + -16 = 0 Reorder the terms: -16 + 39x + 10x2 = 0 Solving -16 + 39x + 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'. -1.6 + 3.9x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 3.9x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 3.9x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 3.9x + x2 = 0 + 1.6 3.9x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 3.9x + x2 = 1.6 The x term is 3.9x. Take half its coefficient (1.95). Square it (3.8025) and add it to both sides. Add '3.8025' to each side of the equation. 3.9x + 3.8025 + x2 = 1.6 + 3.8025 Reorder the terms: 3.8025 + 3.9x + x2 = 1.6 + 3.8025 Combine like terms: 1.6 + 3.8025 = 5.4025 3.8025 + 3.9x + x2 = 5.4025 Factor a perfect square on the left side: (x + 1.95)(x + 1.95) = 5.4025 Calculate the square root of the right side: 2.32432786 Break this problem into two subproblems by setting (x + 1.95) equal to 2.32432786 and -2.32432786.Subproblem 1
x + 1.95 = 2.32432786 Simplifying x + 1.95 = 2.32432786 Reorder the terms: 1.95 + x = 2.32432786 Solving 1.95 + x = 2.32432786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.95' to each side of the equation. 1.95 + -1.95 + x = 2.32432786 + -1.95 Combine like terms: 1.95 + -1.95 = 0.00 0.00 + x = 2.32432786 + -1.95 x = 2.32432786 + -1.95 Combine like terms: 2.32432786 + -1.95 = 0.37432786 x = 0.37432786 Simplifying x = 0.37432786Subproblem 2
x + 1.95 = -2.32432786 Simplifying x + 1.95 = -2.32432786 Reorder the terms: 1.95 + x = -2.32432786 Solving 1.95 + x = -2.32432786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.95' to each side of the equation. 1.95 + -1.95 + x = -2.32432786 + -1.95 Combine like terms: 1.95 + -1.95 = 0.00 0.00 + x = -2.32432786 + -1.95 x = -2.32432786 + -1.95 Combine like terms: -2.32432786 + -1.95 = -4.27432786 x = -4.27432786 Simplifying x = -4.27432786Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.37432786, -4.27432786}
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