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Simplifying 2x2 + 3x = 84 Reorder the terms: 3x + 2x2 = 84 Solving 3x + 2x2 = 84 Solving for variable 'x'. Reorder the terms: -84 + 3x + 2x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -42 + 1.5x + x2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + 1.5x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 1.5x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 1.5x + x2 = 0 + 42 1.5x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 1.5x + x2 = 42 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 42 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 42 + 0.5625 Combine like terms: 42 + 0.5625 = 42.5625 0.5625 + 1.5x + x2 = 42.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 42.5625 Calculate the square root of the right side: 6.523994175 Break this problem into two subproblems by setting (x + 0.75) equal to 6.523994175 and -6.523994175.Subproblem 1
x + 0.75 = 6.523994175 Simplifying x + 0.75 = 6.523994175 Reorder the terms: 0.75 + x = 6.523994175 Solving 0.75 + x = 6.523994175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 6.523994175 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 6.523994175 + -0.75 x = 6.523994175 + -0.75 Combine like terms: 6.523994175 + -0.75 = 5.773994175 x = 5.773994175 Simplifying x = 5.773994175Subproblem 2
x + 0.75 = -6.523994175 Simplifying x + 0.75 = -6.523994175 Reorder the terms: 0.75 + x = -6.523994175 Solving 0.75 + x = -6.523994175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -6.523994175 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -6.523994175 + -0.75 x = -6.523994175 + -0.75 Combine like terms: -6.523994175 + -0.75 = -7.273994175 x = -7.273994175 Simplifying x = -7.273994175Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.773994175, -7.273994175}
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