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Simplifying 49x2 + -28x + -40 = 0 Reorder the terms: -40 + -28x + 49x2 = 0 Solving -40 + -28x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.8163265306 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.8163265306' to each side of the equation. -0.8163265306 + -0.5714285714x + 0.8163265306 + x2 = 0 + 0.8163265306 Reorder the terms: -0.8163265306 + 0.8163265306 + -0.5714285714x + x2 = 0 + 0.8163265306 Combine like terms: -0.8163265306 + 0.8163265306 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + 0.8163265306 -0.5714285714x + x2 = 0 + 0.8163265306 Combine like terms: 0 + 0.8163265306 = 0.8163265306 -0.5714285714x + x2 = 0.8163265306 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 0.8163265306 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 0.8163265306 + 0.08163265305 Combine like terms: 0.8163265306 + 0.08163265305 = 0.89795918365 0.08163265305 + -0.5714285714x + x2 = 0.89795918365 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.89795918365 Calculate the square root of the right side: 0.947607083 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.947607083 and -0.947607083.Subproblem 1
x + -0.2857142857 = 0.947607083 Simplifying x + -0.2857142857 = 0.947607083 Reorder the terms: -0.2857142857 + x = 0.947607083 Solving -0.2857142857 + x = 0.947607083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 0.947607083 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.947607083 + 0.2857142857 x = 0.947607083 + 0.2857142857 Combine like terms: 0.947607083 + 0.2857142857 = 1.2333213687 x = 1.2333213687 Simplifying x = 1.2333213687Subproblem 2
x + -0.2857142857 = -0.947607083 Simplifying x + -0.2857142857 = -0.947607083 Reorder the terms: -0.2857142857 + x = -0.947607083 Solving -0.2857142857 + x = -0.947607083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -0.947607083 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.947607083 + 0.2857142857 x = -0.947607083 + 0.2857142857 Combine like terms: -0.947607083 + 0.2857142857 = -0.6618927973 x = -0.6618927973 Simplifying x = -0.6618927973Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2333213687, -0.6618927973}
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