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Simplifying 10x2 + -3x + -86 = 0 Reorder the terms: -86 + -3x + 10x2 = 0 Solving -86 + -3x + 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'. -8.6 + -0.3x + x2 = 0 Move the constant term to the right: Add '8.6' to each side of the equation. -8.6 + -0.3x + 8.6 + x2 = 0 + 8.6 Reorder the terms: -8.6 + 8.6 + -0.3x + x2 = 0 + 8.6 Combine like terms: -8.6 + 8.6 = 0.0 0.0 + -0.3x + x2 = 0 + 8.6 -0.3x + x2 = 0 + 8.6 Combine like terms: 0 + 8.6 = 8.6 -0.3x + x2 = 8.6 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 8.6 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 8.6 + 0.0225 Combine like terms: 8.6 + 0.0225 = 8.6225 0.0225 + -0.3x + x2 = 8.6225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 8.6225 Calculate the square root of the right side: 2.936409372 Break this problem into two subproblems by setting (x + -0.15) equal to 2.936409372 and -2.936409372.Subproblem 1
x + -0.15 = 2.936409372 Simplifying x + -0.15 = 2.936409372 Reorder the terms: -0.15 + x = 2.936409372 Solving -0.15 + x = 2.936409372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 2.936409372 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 2.936409372 + 0.15 x = 2.936409372 + 0.15 Combine like terms: 2.936409372 + 0.15 = 3.086409372 x = 3.086409372 Simplifying x = 3.086409372Subproblem 2
x + -0.15 = -2.936409372 Simplifying x + -0.15 = -2.936409372 Reorder the terms: -0.15 + x = -2.936409372 Solving -0.15 + x = -2.936409372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -2.936409372 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -2.936409372 + 0.15 x = -2.936409372 + 0.15 Combine like terms: -2.936409372 + 0.15 = -2.786409372 x = -2.786409372 Simplifying x = -2.786409372Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.086409372, -2.786409372}
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