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Simplifying 15x2 + -18x + -34 = 0 Reorder the terms: -34 + -18x + 15x2 = 0 Solving -34 + -18x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -2.266666667 + -1.2x + x2 = 0 Move the constant term to the right: Add '2.266666667' to each side of the equation. -2.266666667 + -1.2x + 2.266666667 + x2 = 0 + 2.266666667 Reorder the terms: -2.266666667 + 2.266666667 + -1.2x + x2 = 0 + 2.266666667 Combine like terms: -2.266666667 + 2.266666667 = 0.000000000 0.000000000 + -1.2x + x2 = 0 + 2.266666667 -1.2x + x2 = 0 + 2.266666667 Combine like terms: 0 + 2.266666667 = 2.266666667 -1.2x + x2 = 2.266666667 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 2.266666667 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 2.266666667 + 0.36 Combine like terms: 2.266666667 + 0.36 = 2.626666667 0.36 + -1.2x + x2 = 2.626666667 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 2.626666667 Calculate the square root of the right side: 1.620699438 Break this problem into two subproblems by setting (x + -0.6) equal to 1.620699438 and -1.620699438.Subproblem 1
x + -0.6 = 1.620699438 Simplifying x + -0.6 = 1.620699438 Reorder the terms: -0.6 + x = 1.620699438 Solving -0.6 + x = 1.620699438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.620699438 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.620699438 + 0.6 x = 1.620699438 + 0.6 Combine like terms: 1.620699438 + 0.6 = 2.220699438 x = 2.220699438 Simplifying x = 2.220699438Subproblem 2
x + -0.6 = -1.620699438 Simplifying x + -0.6 = -1.620699438 Reorder the terms: -0.6 + x = -1.620699438 Solving -0.6 + x = -1.620699438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.620699438 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.620699438 + 0.6 x = -1.620699438 + 0.6 Combine like terms: -1.620699438 + 0.6 = -1.020699438 x = -1.020699438 Simplifying x = -1.020699438Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.220699438, -1.020699438}
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