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Simplifying 10x2 + -17x + -18 = -11 Reorder the terms: -18 + -17x + 10x2 = -11 Solving -18 + -17x + 10x2 = -11 Solving for variable 'x'. Reorder the terms: -18 + 11 + -17x + 10x2 = -11 + 11 Combine like terms: -18 + 11 = -7 -7 + -17x + 10x2 = -11 + 11 Combine like terms: -11 + 11 = 0 -7 + -17x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + -1.7x + x2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + -1.7x + 0.7 + x2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + -1.7x + x2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + -1.7x + x2 = 0 + 0.7 -1.7x + x2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 -1.7x + x2 = 0.7 The x term is -1.7x. Take half its coefficient (-0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. -1.7x + 0.7225 + x2 = 0.7 + 0.7225 Reorder the terms: 0.7225 + -1.7x + x2 = 0.7 + 0.7225 Combine like terms: 0.7 + 0.7225 = 1.4225 0.7225 + -1.7x + x2 = 1.4225 Factor a perfect square on the left side: (x + -0.85)(x + -0.85) = 1.4225 Calculate the square root of the right side: 1.192686044 Break this problem into two subproblems by setting (x + -0.85) equal to 1.192686044 and -1.192686044.Subproblem 1
x + -0.85 = 1.192686044 Simplifying x + -0.85 = 1.192686044 Reorder the terms: -0.85 + x = 1.192686044 Solving -0.85 + x = 1.192686044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + x = 1.192686044 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = 1.192686044 + 0.85 x = 1.192686044 + 0.85 Combine like terms: 1.192686044 + 0.85 = 2.042686044 x = 2.042686044 Simplifying x = 2.042686044Subproblem 2
x + -0.85 = -1.192686044 Simplifying x + -0.85 = -1.192686044 Reorder the terms: -0.85 + x = -1.192686044 Solving -0.85 + x = -1.192686044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + x = -1.192686044 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = -1.192686044 + 0.85 x = -1.192686044 + 0.85 Combine like terms: -1.192686044 + 0.85 = -0.342686044 x = -0.342686044 Simplifying x = -0.342686044Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.042686044, -0.342686044}
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