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Simplifying 10x2 + -3x = 8 Reorder the terms: -3x + 10x2 = 8 Solving -3x + 10x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -3x + 10x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.8 + -0.3x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.3x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.3x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.3x + x2 = 0 + 0.8 -0.3x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.3x + x2 = 0.8 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 = 0.8 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 0.8 + 0.0225 Combine like terms: 0.8 + 0.0225 = 0.8225 0.0225 + -0.3x + x2 = 0.8225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 0.8225 Calculate the square root of the right side: 0.906917857 Break this problem into two subproblems by setting (x + -0.15) equal to 0.906917857 and -0.906917857.Subproblem 1
x + -0.15 = 0.906917857 Simplifying x + -0.15 = 0.906917857 Reorder the terms: -0.15 + x = 0.906917857 Solving -0.15 + x = 0.906917857 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 = 0.906917857 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.906917857 + 0.15 x = 0.906917857 + 0.15 Combine like terms: 0.906917857 + 0.15 = 1.056917857 x = 1.056917857 Simplifying x = 1.056917857Subproblem 2
x + -0.15 = -0.906917857 Simplifying x + -0.15 = -0.906917857 Reorder the terms: -0.15 + x = -0.906917857 Solving -0.15 + x = -0.906917857 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 = -0.906917857 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.906917857 + 0.15 x = -0.906917857 + 0.15 Combine like terms: -0.906917857 + 0.15 = -0.756917857 x = -0.756917857 Simplifying x = -0.756917857Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.056917857, -0.756917857}
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