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Simplifying 4.1 = -0.5x2 + 1x + 12 Reorder the terms: 4.1 = 12 + 1x + -0.5x2 Solving 4.1 = 12 + 1x + -0.5x2 Solving for variable 'x'. Combine like terms: 4.1 + -12 = -7.9 -7.9 + -1x + 0.5x2 = 12 + 1x + -0.5x2 + -12 + -1x + 0.5x2 Reorder the terms: -7.9 + -1x + 0.5x2 = 12 + -12 + 1x + -1x + -0.5x2 + 0.5x2 Combine like terms: 12 + -12 = 0 -7.9 + -1x + 0.5x2 = 0 + 1x + -1x + -0.5x2 + 0.5x2 -7.9 + -1x + 0.5x2 = 1x + -1x + -0.5x2 + 0.5x2 Combine like terms: 1x + -1x = 0 -7.9 + -1x + 0.5x2 = 0 + -0.5x2 + 0.5x2 -7.9 + -1x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -7.9 + -1x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -15.8 + -2x + x2 = 0 Move the constant term to the right: Add '15.8' to each side of the equation. -15.8 + -2x + 15.8 + x2 = 0 + 15.8 Reorder the terms: -15.8 + 15.8 + -2x + x2 = 0 + 15.8 Combine like terms: -15.8 + 15.8 = 0.0 0.0 + -2x + x2 = 0 + 15.8 -2x + x2 = 0 + 15.8 Combine like terms: 0 + 15.8 = 15.8 -2x + x2 = 15.8 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 15.8 + 1 Reorder the terms: 1 + -2x + x2 = 15.8 + 1 Combine like terms: 15.8 + 1 = 16.8 1 + -2x + x2 = 16.8 Factor a perfect square on the left side: (x + -1)(x + -1) = 16.8 Calculate the square root of the right side: 4.098780306 Break this problem into two subproblems by setting (x + -1) equal to 4.098780306 and -4.098780306.Subproblem 1
x + -1 = 4.098780306 Simplifying x + -1 = 4.098780306 Reorder the terms: -1 + x = 4.098780306 Solving -1 + x = 4.098780306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.098780306 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.098780306 + 1 x = 4.098780306 + 1 Combine like terms: 4.098780306 + 1 = 5.098780306 x = 5.098780306 Simplifying x = 5.098780306Subproblem 2
x + -1 = -4.098780306 Simplifying x + -1 = -4.098780306 Reorder the terms: -1 + x = -4.098780306 Solving -1 + x = -4.098780306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.098780306 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.098780306 + 1 x = -4.098780306 + 1 Combine like terms: -4.098780306 + 1 = -3.098780306 x = -3.098780306 Simplifying x = -3.098780306Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.098780306, -3.098780306}
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