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Simplifying 10x2 + 39x + 28 = 0 Reorder the terms: 28 + 39x + 10x2 = 0 Solving 28 + 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'. 2.8 + 3.9x + x2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + 3.9x + -2.8 + x2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + 3.9x + x2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 3.9x + x2 = 0 + -2.8 3.9x + x2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 3.9x + x2 = -2.8 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 = -2.8 + 3.8025 Reorder the terms: 3.8025 + 3.9x + x2 = -2.8 + 3.8025 Combine like terms: -2.8 + 3.8025 = 1.0025 3.8025 + 3.9x + x2 = 1.0025 Factor a perfect square on the left side: (x + 1.95)(x + 1.95) = 1.0025 Calculate the square root of the right side: 1.00124922 Break this problem into two subproblems by setting (x + 1.95) equal to 1.00124922 and -1.00124922.Subproblem 1
x + 1.95 = 1.00124922 Simplifying x + 1.95 = 1.00124922 Reorder the terms: 1.95 + x = 1.00124922 Solving 1.95 + x = 1.00124922 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 = 1.00124922 + -1.95 Combine like terms: 1.95 + -1.95 = 0.00 0.00 + x = 1.00124922 + -1.95 x = 1.00124922 + -1.95 Combine like terms: 1.00124922 + -1.95 = -0.94875078 x = -0.94875078 Simplifying x = -0.94875078Subproblem 2
x + 1.95 = -1.00124922 Simplifying x + 1.95 = -1.00124922 Reorder the terms: 1.95 + x = -1.00124922 Solving 1.95 + x = -1.00124922 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 = -1.00124922 + -1.95 Combine like terms: 1.95 + -1.95 = 0.00 0.00 + x = -1.00124922 + -1.95 x = -1.00124922 + -1.95 Combine like terms: -1.00124922 + -1.95 = -2.95124922 x = -2.95124922 Simplifying x = -2.95124922Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.94875078, -2.95124922}
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