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Simplifying 7x2 + 8x + -18 + -9 + 14x = 0 Reorder the terms: -18 + -9 + 8x + 14x + 7x2 = 0 Combine like terms: -18 + -9 = -27 -27 + 8x + 14x + 7x2 = 0 Combine like terms: 8x + 14x = 22x -27 + 22x + 7x2 = 0 Solving -27 + 22x + 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'. -3.857142857 + 3.142857143x + x2 = 0 Move the constant term to the right: Add '3.857142857' to each side of the equation. -3.857142857 + 3.142857143x + 3.857142857 + x2 = 0 + 3.857142857 Reorder the terms: -3.857142857 + 3.857142857 + 3.142857143x + x2 = 0 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + 3.142857143x + x2 = 0 + 3.857142857 3.142857143x + x2 = 0 + 3.857142857 Combine like terms: 0 + 3.857142857 = 3.857142857 3.142857143x + x2 = 3.857142857 The x term is 3.142857143x. Take half its coefficient (1.571428572). Square it (2.469387757) and add it to both sides. Add '2.469387757' to each side of the equation. 3.142857143x + 2.469387757 + x2 = 3.857142857 + 2.469387757 Reorder the terms: 2.469387757 + 3.142857143x + x2 = 3.857142857 + 2.469387757 Combine like terms: 3.857142857 + 2.469387757 = 6.326530614 2.469387757 + 3.142857143x + x2 = 6.326530614 Factor a perfect square on the left side: (x + 1.571428572)(x + 1.571428572) = 6.326530614 Calculate the square root of the right side: 2.515259552 Break this problem into two subproblems by setting (x + 1.571428572) equal to 2.515259552 and -2.515259552.Subproblem 1
x + 1.571428572 = 2.515259552 Simplifying x + 1.571428572 = 2.515259552 Reorder the terms: 1.571428572 + x = 2.515259552 Solving 1.571428572 + x = 2.515259552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = 2.515259552 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = 2.515259552 + -1.571428572 x = 2.515259552 + -1.571428572 Combine like terms: 2.515259552 + -1.571428572 = 0.94383098 x = 0.94383098 Simplifying x = 0.94383098Subproblem 2
x + 1.571428572 = -2.515259552 Simplifying x + 1.571428572 = -2.515259552 Reorder the terms: 1.571428572 + x = -2.515259552 Solving 1.571428572 + x = -2.515259552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = -2.515259552 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = -2.515259552 + -1.571428572 x = -2.515259552 + -1.571428572 Combine like terms: -2.515259552 + -1.571428572 = -4.086688124 x = -4.086688124 Simplifying x = -4.086688124Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.94383098, -4.086688124}
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