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Simplifying 10x2 + 2x + -2907 = 0 Reorder the terms: -2907 + 2x + 10x2 = 0 Solving -2907 + 2x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -290.7 + 0.2x + x2 = 0 Move the constant term to the right: Add '290.7' to each side of the equation. -290.7 + 0.2x + 290.7 + x2 = 0 + 290.7 Reorder the terms: -290.7 + 290.7 + 0.2x + x2 = 0 + 290.7 Combine like terms: -290.7 + 290.7 = 0.0 0.0 + 0.2x + x2 = 0 + 290.7 0.2x + x2 = 0 + 290.7 Combine like terms: 0 + 290.7 = 290.7 0.2x + x2 = 290.7 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 290.7 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 290.7 + 0.01 Combine like terms: 290.7 + 0.01 = 290.71 0.01 + 0.2x + x2 = 290.71 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 290.71 Calculate the square root of the right side: 17.05021994 Break this problem into two subproblems by setting (x + 0.1) equal to 17.05021994 and -17.05021994.Subproblem 1
x + 0.1 = 17.05021994 Simplifying x + 0.1 = 17.05021994 Reorder the terms: 0.1 + x = 17.05021994 Solving 0.1 + x = 17.05021994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 17.05021994 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 17.05021994 + -0.1 x = 17.05021994 + -0.1 Combine like terms: 17.05021994 + -0.1 = 16.95021994 x = 16.95021994 Simplifying x = 16.95021994Subproblem 2
x + 0.1 = -17.05021994 Simplifying x + 0.1 = -17.05021994 Reorder the terms: 0.1 + x = -17.05021994 Solving 0.1 + x = -17.05021994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -17.05021994 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -17.05021994 + -0.1 x = -17.05021994 + -0.1 Combine like terms: -17.05021994 + -0.1 = -17.15021994 x = -17.15021994 Simplifying x = -17.15021994Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.95021994, -17.15021994}
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