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Simplifying 18x2 + -12x + 2 = 7 Reorder the terms: 2 + -12x + 18x2 = 7 Solving 2 + -12x + 18x2 = 7 Solving for variable 'x'. Reorder the terms: 2 + -7 + -12x + 18x2 = 7 + -7 Combine like terms: 2 + -7 = -5 -5 + -12x + 18x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -5 + -12x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2777777778 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + -0.6666666667x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + -0.6666666667x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + -0.6666666667x + x2 = 0 + 0.2777777778 -0.6666666667x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 -0.6666666667x + x2 = 0.2777777778 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 0.2777777778 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 0.2777777778 + 0.1111111112 Combine like terms: 0.2777777778 + 0.1111111112 = 0.388888889 0.1111111112 + -0.6666666667x + x2 = 0.388888889 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 0.388888889 Calculate the square root of the right side: 0.623609565 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 0.623609565 and -0.623609565.Subproblem 1
x + -0.3333333334 = 0.623609565 Simplifying x + -0.3333333334 = 0.623609565 Reorder the terms: -0.3333333334 + x = 0.623609565 Solving -0.3333333334 + x = 0.623609565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 0.623609565 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.623609565 + 0.3333333334 x = 0.623609565 + 0.3333333334 Combine like terms: 0.623609565 + 0.3333333334 = 0.9569428984 x = 0.9569428984 Simplifying x = 0.9569428984Subproblem 2
x + -0.3333333334 = -0.623609565 Simplifying x + -0.3333333334 = -0.623609565 Reorder the terms: -0.3333333334 + x = -0.623609565 Solving -0.3333333334 + x = -0.623609565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -0.623609565 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.623609565 + 0.3333333334 x = -0.623609565 + 0.3333333334 Combine like terms: -0.623609565 + 0.3333333334 = -0.2902762316 x = -0.2902762316 Simplifying x = -0.2902762316Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9569428984, -0.2902762316}
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