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Simplifying 49 = 42x + 4x2 Solving 49 = 42x + 4x2 Solving for variable 'x'. Reorder the terms: 49 + -42x + -4x2 = 42x + -42x + 4x2 + -4x2 Combine like terms: 42x + -42x = 0 49 + -42x + -4x2 = 0 + 4x2 + -4x2 49 + -42x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 49 + -42x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -12.25 + 10.5x + x2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + 10.5x + 12.25 + x2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + 10.5x + x2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + 10.5x + x2 = 0 + 12.25 10.5x + x2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 10.5x + x2 = 12.25 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 12.25 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 12.25 + 27.5625 Combine like terms: 12.25 + 27.5625 = 39.8125 27.5625 + 10.5x + x2 = 39.8125 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 39.8125 Calculate the square root of the right side: 6.309714732 Break this problem into two subproblems by setting (x + 5.25) equal to 6.309714732 and -6.309714732.Subproblem 1
x + 5.25 = 6.309714732 Simplifying x + 5.25 = 6.309714732 Reorder the terms: 5.25 + x = 6.309714732 Solving 5.25 + x = 6.309714732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 6.309714732 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 6.309714732 + -5.25 x = 6.309714732 + -5.25 Combine like terms: 6.309714732 + -5.25 = 1.059714732 x = 1.059714732 Simplifying x = 1.059714732Subproblem 2
x + 5.25 = -6.309714732 Simplifying x + 5.25 = -6.309714732 Reorder the terms: 5.25 + x = -6.309714732 Solving 5.25 + x = -6.309714732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -6.309714732 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -6.309714732 + -5.25 x = -6.309714732 + -5.25 Combine like terms: -6.309714732 + -5.25 = -11.559714732 x = -11.559714732 Simplifying x = -11.559714732Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.059714732, -11.559714732}
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