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Simplifying 9x2 + -43 = 18x Reorder the terms: -43 + 9x2 = 18x Solving -43 + 9x2 = 18x Solving for variable 'x'. Reorder the terms: -43 + -18x + 9x2 = 18x + -18x Combine like terms: 18x + -18x = 0 -43 + -18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4.777777778 + -2x + x2 = 0 Move the constant term to the right: Add '4.777777778' to each side of the equation. -4.777777778 + -2x + 4.777777778 + x2 = 0 + 4.777777778 Reorder the terms: -4.777777778 + 4.777777778 + -2x + x2 = 0 + 4.777777778 Combine like terms: -4.777777778 + 4.777777778 = 0.000000000 0.000000000 + -2x + x2 = 0 + 4.777777778 -2x + x2 = 0 + 4.777777778 Combine like terms: 0 + 4.777777778 = 4.777777778 -2x + x2 = 4.777777778 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 4.777777778 + 1 Reorder the terms: 1 + -2x + x2 = 4.777777778 + 1 Combine like terms: 4.777777778 + 1 = 5.777777778 1 + -2x + x2 = 5.777777778 Factor a perfect square on the left side: (x + -1)(x + -1) = 5.777777778 Calculate the square root of the right side: 2.40370085 Break this problem into two subproblems by setting (x + -1) equal to 2.40370085 and -2.40370085.Subproblem 1
x + -1 = 2.40370085 Simplifying x + -1 = 2.40370085 Reorder the terms: -1 + x = 2.40370085 Solving -1 + x = 2.40370085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.40370085 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.40370085 + 1 x = 2.40370085 + 1 Combine like terms: 2.40370085 + 1 = 3.40370085 x = 3.40370085 Simplifying x = 3.40370085Subproblem 2
x + -1 = -2.40370085 Simplifying x + -1 = -2.40370085 Reorder the terms: -1 + x = -2.40370085 Solving -1 + x = -2.40370085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.40370085 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.40370085 + 1 x = -2.40370085 + 1 Combine like terms: -2.40370085 + 1 = -1.40370085 x = -1.40370085 Simplifying x = -1.40370085Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.40370085, -1.40370085}
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