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Simplifying 5x2 + 30x = 12.8 Reorder the terms: 30x + 5x2 = 12.8 Solving 30x + 5x2 = 12.8 Solving for variable 'x'. Reorder the terms: -12.8 + 30x + 5x2 = 12.8 + -12.8 Combine like terms: 12.8 + -12.8 = 0.0 -12.8 + 30x + 5x2 = 0.0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.56 + 6x + x2 = 0.0 Move the constant term to the right: Add '2.56' to each side of the equation. -2.56 + 6x + 2.56 + x2 = 0.0 + 2.56 Reorder the terms: -2.56 + 2.56 + 6x + x2 = 0.0 + 2.56 Combine like terms: -2.56 + 2.56 = 0.00 0.00 + 6x + x2 = 0.0 + 2.56 6x + x2 = 0.0 + 2.56 Combine like terms: 0.0 + 2.56 = 2.56 6x + x2 = 2.56 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 2.56 + 9 Reorder the terms: 9 + 6x + x2 = 2.56 + 9 Combine like terms: 2.56 + 9 = 11.56 9 + 6x + x2 = 11.56 Factor a perfect square on the left side: (x + 3)(x + 3) = 11.56 Calculate the square root of the right side: 3.4 Break this problem into two subproblems by setting (x + 3) equal to 3.4 and -3.4.Subproblem 1
x + 3 = 3.4 Simplifying x + 3 = 3.4 Reorder the terms: 3 + x = 3.4 Solving 3 + x = 3.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.4 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.4 + -3 x = 3.4 + -3 Combine like terms: 3.4 + -3 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + 3 = -3.4 Simplifying x + 3 = -3.4 Reorder the terms: 3 + x = -3.4 Solving 3 + x = -3.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.4 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.4 + -3 x = -3.4 + -3 Combine like terms: -3.4 + -3 = -6.4 x = -6.4 Simplifying x = -6.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4, -6.4}
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