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Simplifying 30 = (4x2) + 3x Reorder the terms: 30 = 3x + (4x2) Solving 30 = 3x + (4x2) Solving for variable 'x'. Reorder the terms: 30 + -3x + (-4x2) = 3x + -3x + (4x2) + (-4x2) Combine like terms: 3x + -3x = 0 30 + -3x + (-4x2) = 0 + (4x2) + (-4x2) 30 + -3x + (-4x2) = (4x2) + (-4x2) Combine like terms: (4x2) + (-4x2) = 0 30 + -3x + (-4x2) = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -7.5 + 0.75x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 0.75x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 0.75x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 0.75x + x2 = 0 + 7.5 0.75x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 0.75x + x2 = 7.5 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 7.5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 7.5 + 0.140625 Combine like terms: 7.5 + 0.140625 = 7.640625 0.140625 + 0.75x + x2 = 7.640625 Factor a perfect square on the left side: ((x) + 0.375)((x) + 0.375) = 7.640625 Calculate the square root of the right side: 2.764168048 Break this problem into two subproblems by setting ((x) + 0.375) equal to 2.764168048 and -2.764168048.Subproblem 1
(x) + 0.375 = 2.764168048 Simplifying (x) + 0.375 = 2.764168048 x + 0.375 = 2.764168048 Reorder the terms: 0.375 + x = 2.764168048 Solving 0.375 + x = 2.764168048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 2.764168048 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 2.764168048 + -0.375 x = 2.764168048 + -0.375 Combine like terms: 2.764168048 + -0.375 = 2.389168048 x = 2.389168048 Simplifying x = 2.389168048Subproblem 2
(x) + 0.375 = -2.764168048 Simplifying (x) + 0.375 = -2.764168048 x + 0.375 = -2.764168048 Reorder the terms: 0.375 + x = -2.764168048 Solving 0.375 + x = -2.764168048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -2.764168048 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -2.764168048 + -0.375 x = -2.764168048 + -0.375 Combine like terms: -2.764168048 + -0.375 = -3.139168048 x = -3.139168048 Simplifying x = -3.139168048Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.389168048, -3.139168048}
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