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Simplifying 1.4x2 + 5.6x + -16.8 = 0 Reorder the terms: -16.8 + 5.6x + 1.4x2 = 0 Solving -16.8 + 5.6x + 1.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. -12 + 4x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 4x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 4x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 4x + x2 = 0 + 12 4x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 4x + x2 = 12 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 12 + 4 Reorder the terms: 4 + 4x + x2 = 12 + 4 Combine like terms: 12 + 4 = 16 4 + 4x + x2 = 16 Factor a perfect square on the left side: (x + 2)(x + 2) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + 2) equal to 4 and -4.Subproblem 1
x + 2 = 4 Simplifying x + 2 = 4 Reorder the terms: 2 + x = 4 Solving 2 + x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4 + -2 x = 4 + -2 Combine like terms: 4 + -2 = 2 x = 2 Simplifying x = 2Subproblem 2
x + 2 = -4 Simplifying x + 2 = -4 Reorder the terms: 2 + x = -4 Solving 2 + x = -4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4 + -2 x = -4 + -2 Combine like terms: -4 + -2 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -6}
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