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Simplifying 5x + -1((0.5) * x2) + -2.75 = 0 Remove parenthesis around (0.5x2) 5x + -1 * 0.5x2 + -2.75 = 0 Multiply -1 * 0.5 5x + -0.5x2 + -2.75 = 0 Reorder the terms: -2.75 + 5x + -0.5x2 = 0 Solving -2.75 + 5x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 5.5 + -10x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -10x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -10x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -10x + x2 = 0 + -5.5 -10x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -10x + x2 = -5.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -5.5 + 25 Reorder the terms: 25 + -10x + x2 = -5.5 + 25 Combine like terms: -5.5 + 25 = 19.5 25 + -10x + x2 = 19.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 19.5 Calculate the square root of the right side: 4.415880433 Break this problem into two subproblems by setting (x + -5) equal to 4.415880433 and -4.415880433.Subproblem 1
x + -5 = 4.415880433 Simplifying x + -5 = 4.415880433 Reorder the terms: -5 + x = 4.415880433 Solving -5 + x = 4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.415880433 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.415880433 + 5 x = 4.415880433 + 5 Combine like terms: 4.415880433 + 5 = 9.415880433 x = 9.415880433 Simplifying x = 9.415880433Subproblem 2
x + -5 = -4.415880433 Simplifying x + -5 = -4.415880433 Reorder the terms: -5 + x = -4.415880433 Solving -5 + x = -4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.415880433 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.415880433 + 5 x = -4.415880433 + 5 Combine like terms: -4.415880433 + 5 = 0.584119567 x = 0.584119567 Simplifying x = 0.584119567Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.415880433, 0.584119567}
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