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Simplifying (-5x2) + 28x = 12 Reorder the terms: 28x + (-5x2) = 12 Solving 28x + (-5x2) = 12 Solving for variable 'x'. Reorder the terms: -12 + 28x + (-5x2) = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 28x + (-5x2) = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 2.4 + -5.6x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -5.6x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -5.6x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -5.6x + x2 = 0 + -2.4 -5.6x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -5.6x + x2 = -2.4 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = -2.4 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = -2.4 + 7.84 Combine like terms: -2.4 + 7.84 = 5.44 7.84 + -5.6x + x2 = 5.44 Factor a perfect square on the left side: ((x) + -2.8)((x) + -2.8) = 5.44 Calculate the square root of the right side: 2.332380758 Break this problem into two subproblems by setting ((x) + -2.8) equal to 2.332380758 and -2.332380758.Subproblem 1
(x) + -2.8 = 2.332380758 Simplifying (x) + -2.8 = 2.332380758 x + -2.8 = 2.332380758 Reorder the terms: -2.8 + x = 2.332380758 Solving -2.8 + x = 2.332380758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 2.332380758 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 2.332380758 + 2.8 x = 2.332380758 + 2.8 Combine like terms: 2.332380758 + 2.8 = 5.132380758 x = 5.132380758 Simplifying x = 5.132380758Subproblem 2
(x) + -2.8 = -2.332380758 Simplifying (x) + -2.8 = -2.332380758 x + -2.8 = -2.332380758 Reorder the terms: -2.8 + x = -2.332380758 Solving -2.8 + x = -2.332380758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -2.332380758 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -2.332380758 + 2.8 x = -2.332380758 + 2.8 Combine like terms: -2.332380758 + 2.8 = 0.467619242 x = 0.467619242 Simplifying x = 0.467619242Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.132380758, 0.467619242}
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