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Simplifying -5X2 + -1X + 3 = 0 Reorder the terms: 3 + -1X + -5X2 = 0 Solving 3 + -1X + -5X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.6 + 0.2X + X2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 0.2X + 0.6 + X2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 0.2X + X2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 0.2X + X2 = 0 + 0.6 0.2X + X2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 0.2X + X2 = 0.6 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 = 0.6 + 0.01 Reorder the terms: 0.01 + 0.2X + X2 = 0.6 + 0.01 Combine like terms: 0.6 + 0.01 = 0.61 0.01 + 0.2X + X2 = 0.61 Factor a perfect square on the left side: (X + 0.1)(X + 0.1) = 0.61 Calculate the square root of the right side: 0.781024968 Break this problem into two subproblems by setting (X + 0.1) equal to 0.781024968 and -0.781024968.Subproblem 1
X + 0.1 = 0.781024968 Simplifying X + 0.1 = 0.781024968 Reorder the terms: 0.1 + X = 0.781024968 Solving 0.1 + X = 0.781024968 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 = 0.781024968 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + X = 0.781024968 + -0.1 X = 0.781024968 + -0.1 Combine like terms: 0.781024968 + -0.1 = 0.681024968 X = 0.681024968 Simplifying X = 0.681024968Subproblem 2
X + 0.1 = -0.781024968 Simplifying X + 0.1 = -0.781024968 Reorder the terms: 0.1 + X = -0.781024968 Solving 0.1 + X = -0.781024968 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 = -0.781024968 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + X = -0.781024968 + -0.1 X = -0.781024968 + -0.1 Combine like terms: -0.781024968 + -0.1 = -0.881024968 X = -0.881024968 Simplifying X = -0.881024968Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.681024968, -0.881024968}
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