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Simplifying 7x2 + 4x + -8 = 14 Reorder the terms: -8 + 4x + 7x2 = 14 Solving -8 + 4x + 7x2 = 14 Solving for variable 'x'. Reorder the terms: -8 + -14 + 4x + 7x2 = 14 + -14 Combine like terms: -8 + -14 = -22 -22 + 4x + 7x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -22 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.142857143 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '3.142857143' to each side of the equation. -3.142857143 + 0.5714285714x + 3.142857143 + x2 = 0 + 3.142857143 Reorder the terms: -3.142857143 + 3.142857143 + 0.5714285714x + x2 = 0 + 3.142857143 Combine like terms: -3.142857143 + 3.142857143 = 0.000000000 0.000000000 + 0.5714285714x + x2 = 0 + 3.142857143 0.5714285714x + x2 = 0 + 3.142857143 Combine like terms: 0 + 3.142857143 = 3.142857143 0.5714285714x + x2 = 3.142857143 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 = 3.142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 3.142857143 + 0.08163265305 Combine like terms: 3.142857143 + 0.08163265305 = 3.22448979605 0.08163265305 + 0.5714285714x + x2 = 3.22448979605 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 3.22448979605 Calculate the square root of the right side: 1.795686441 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 1.795686441 and -1.795686441.Subproblem 1
x + 0.2857142857 = 1.795686441 Simplifying x + 0.2857142857 = 1.795686441 Reorder the terms: 0.2857142857 + x = 1.795686441 Solving 0.2857142857 + x = 1.795686441 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 = 1.795686441 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 1.795686441 + -0.2857142857 x = 1.795686441 + -0.2857142857 Combine like terms: 1.795686441 + -0.2857142857 = 1.5099721553 x = 1.5099721553 Simplifying x = 1.5099721553Subproblem 2
x + 0.2857142857 = -1.795686441 Simplifying x + 0.2857142857 = -1.795686441 Reorder the terms: 0.2857142857 + x = -1.795686441 Solving 0.2857142857 + x = -1.795686441 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 = -1.795686441 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -1.795686441 + -0.2857142857 x = -1.795686441 + -0.2857142857 Combine like terms: -1.795686441 + -0.2857142857 = -2.0814007267 x = -2.0814007267 Simplifying x = -2.0814007267Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5099721553, -2.0814007267}
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