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Simplifying 7x2 + 12x + -2 = 0 Reorder the terms: -2 + 12x + 7x2 = 0 Solving -2 + 12x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 1.714285714x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 1.714285714x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 1.714285714x + x2 = 0 + 0.2857142857 1.714285714x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 1.714285714x + x2 = 0.2857142857 The x term is 1.714285714x. Take half its coefficient (0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. 1.714285714x + 0.7346938773 + x2 = 0.2857142857 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = 0.2857142857 + 0.7346938773 Combine like terms: 0.2857142857 + 0.7346938773 = 1.020408163 0.7346938773 + 1.714285714x + x2 = 1.020408163 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 1.020408163 Calculate the square root of the right side: 1.010152544 Break this problem into two subproblems by setting (x + 0.857142857) equal to 1.010152544 and -1.010152544.Subproblem 1
x + 0.857142857 = 1.010152544 Simplifying x + 0.857142857 = 1.010152544 Reorder the terms: 0.857142857 + x = 1.010152544 Solving 0.857142857 + x = 1.010152544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = 1.010152544 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 1.010152544 + -0.857142857 x = 1.010152544 + -0.857142857 Combine like terms: 1.010152544 + -0.857142857 = 0.153009687 x = 0.153009687 Simplifying x = 0.153009687Subproblem 2
x + 0.857142857 = -1.010152544 Simplifying x + 0.857142857 = -1.010152544 Reorder the terms: 0.857142857 + x = -1.010152544 Solving 0.857142857 + x = -1.010152544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = -1.010152544 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -1.010152544 + -0.857142857 x = -1.010152544 + -0.857142857 Combine like terms: -1.010152544 + -0.857142857 = -1.867295401 x = -1.867295401 Simplifying x = -1.867295401Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.153009687, -1.867295401}
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