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Simplifying 4X2 + 10X = -1X2 + -1X + 4 Reorder the terms: 10X + 4X2 = -1X2 + -1X + 4 Reorder the terms: 10X + 4X2 = 4 + -1X + -1X2 Solving 10X + 4X2 = 4 + -1X + -1X2 Solving for variable 'X'. Reorder the terms: -4 + 10X + X + 4X2 + X2 = 4 + -1X + -1X2 + -4 + X + X2 Combine like terms: 10X + X = 11X -4 + 11X + 4X2 + X2 = 4 + -1X + -1X2 + -4 + X + X2 Combine like terms: 4X2 + X2 = 5X2 -4 + 11X + 5X2 = 4 + -1X + -1X2 + -4 + X + X2 Reorder the terms: -4 + 11X + 5X2 = 4 + -4 + -1X + X + -1X2 + X2 Combine like terms: 4 + -4 = 0 -4 + 11X + 5X2 = 0 + -1X + X + -1X2 + X2 -4 + 11X + 5X2 = -1X + X + -1X2 + X2 Combine like terms: -1X + X = 0 -4 + 11X + 5X2 = 0 + -1X2 + X2 -4 + 11X + 5X2 = -1X2 + X2 Combine like terms: -1X2 + X2 = 0 -4 + 11X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 2.2X + X2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 2.2X + 0.8 + X2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 2.2X + X2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 2.2X + X2 = 0 + 0.8 2.2X + X2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 2.2X + X2 = 0.8 The X term is 2.2X. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2X + 1.21 + X2 = 0.8 + 1.21 Reorder the terms: 1.21 + 2.2X + X2 = 0.8 + 1.21 Combine like terms: 0.8 + 1.21 = 2.01 1.21 + 2.2X + X2 = 2.01 Factor a perfect square on the left side: (X + 1.1)(X + 1.1) = 2.01 Calculate the square root of the right side: 1.417744688 Break this problem into two subproblems by setting (X + 1.1) equal to 1.417744688 and -1.417744688.Subproblem 1
X + 1.1 = 1.417744688 Simplifying X + 1.1 = 1.417744688 Reorder the terms: 1.1 + X = 1.417744688 Solving 1.1 + X = 1.417744688 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + X = 1.417744688 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + X = 1.417744688 + -1.1 X = 1.417744688 + -1.1 Combine like terms: 1.417744688 + -1.1 = 0.317744688 X = 0.317744688 Simplifying X = 0.317744688Subproblem 2
X + 1.1 = -1.417744688 Simplifying X + 1.1 = -1.417744688 Reorder the terms: 1.1 + X = -1.417744688 Solving 1.1 + X = -1.417744688 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + X = -1.417744688 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + X = -1.417744688 + -1.1 X = -1.417744688 + -1.1 Combine like terms: -1.417744688 + -1.1 = -2.517744688 X = -2.517744688 Simplifying X = -2.517744688Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.317744688, -2.517744688}
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