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Simplifying 1x(3 + 7x) = 191 (3 * 1x + 7x * 1x) = 191 (3x + 7x2) = 191 Solving 3x + 7x2 = 191 Solving for variable 'x'. Reorder the terms: -191 + 3x + 7x2 = 191 + -191 Combine like terms: 191 + -191 = 0 -191 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -27.28571429 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '27.28571429' to each side of the equation. -27.28571429 + 0.4285714286x + 27.28571429 + x2 = 0 + 27.28571429 Reorder the terms: -27.28571429 + 27.28571429 + 0.4285714286x + x2 = 0 + 27.28571429 Combine like terms: -27.28571429 + 27.28571429 = 0.00000000 0.00000000 + 0.4285714286x + x2 = 0 + 27.28571429 0.4285714286x + x2 = 0 + 27.28571429 Combine like terms: 0 + 27.28571429 = 27.28571429 0.4285714286x + x2 = 27.28571429 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 27.28571429 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 27.28571429 + 0.04591836735 Combine like terms: 27.28571429 + 0.04591836735 = 27.33163265735 0.04591836735 + 0.4285714286x + x2 = 27.33163265735 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 27.33163265735 Calculate the square root of the right side: 5.227966398 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 5.227966398 and -5.227966398.Subproblem 1
x + 0.2142857143 = 5.227966398 Simplifying x + 0.2142857143 = 5.227966398 Reorder the terms: 0.2142857143 + x = 5.227966398 Solving 0.2142857143 + x = 5.227966398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 5.227966398 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 5.227966398 + -0.2142857143 x = 5.227966398 + -0.2142857143 Combine like terms: 5.227966398 + -0.2142857143 = 5.0136806837 x = 5.0136806837 Simplifying x = 5.0136806837Subproblem 2
x + 0.2142857143 = -5.227966398 Simplifying x + 0.2142857143 = -5.227966398 Reorder the terms: 0.2142857143 + x = -5.227966398 Solving 0.2142857143 + x = -5.227966398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -5.227966398 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -5.227966398 + -0.2142857143 x = -5.227966398 + -0.2142857143 Combine like terms: -5.227966398 + -0.2142857143 = -5.4422521123 x = -5.4422521123 Simplifying x = -5.4422521123Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.0136806837, -5.4422521123}
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