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Simplifying -2.8 = 2x2 + -4.8x Reorder the terms: -2.8 = -4.8x + 2x2 Solving -2.8 = -4.8x + 2x2 Solving for variable 'x'. Reorder the terms: -2.8 + 4.8x + -2x2 = -4.8x + 4.8x + 2x2 + -2x2 Combine like terms: -4.8x + 4.8x = 0.0 -2.8 + 4.8x + -2x2 = 0.0 + 2x2 + -2x2 -2.8 + 4.8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -2.8 + 4.8x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.4 + -2.4x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -2.4x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -2.4x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -2.4x + x2 = 0 + -1.4 -2.4x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -2.4x + x2 = -1.4 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -1.4 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -1.4 + 1.44 Combine like terms: -1.4 + 1.44 = 0.04 1.44 + -2.4x + x2 = 0.04 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.04 Calculate the square root of the right side: 0.2 Break this problem into two subproblems by setting (x + -1.2) equal to 0.2 and -0.2.Subproblem 1
x + -1.2 = 0.2 Simplifying x + -1.2 = 0.2 Reorder the terms: -1.2 + x = 0.2 Solving -1.2 + x = 0.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 0.2 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.2 + 1.2 x = 0.2 + 1.2 Combine like terms: 0.2 + 1.2 = 1.4 x = 1.4 Simplifying x = 1.4Subproblem 2
x + -1.2 = -0.2 Simplifying x + -1.2 = -0.2 Reorder the terms: -1.2 + x = -0.2 Solving -1.2 + x = -0.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -0.2 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.2 + 1.2 x = -0.2 + 1.2 Combine like terms: -0.2 + 1.2 = 1 x = 1 Simplifying x = 1Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4, 1}
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