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Simplifying 4.8 = 2x2 + -2.6x + 0.72 Reorder the terms: 4.8 = 0.72 + -2.6x + 2x2 Solving 4.8 = 0.72 + -2.6x + 2x2 Solving for variable 'x'. Combine like terms: 4.8 + -0.72 = 4.08 4.08 + 2.6x + -2x2 = 0.72 + -2.6x + 2x2 + -0.72 + 2.6x + -2x2 Reorder the terms: 4.08 + 2.6x + -2x2 = 0.72 + -0.72 + -2.6x + 2.6x + 2x2 + -2x2 Combine like terms: 0.72 + -0.72 = 0.00 4.08 + 2.6x + -2x2 = 0.00 + -2.6x + 2.6x + 2x2 + -2x2 4.08 + 2.6x + -2x2 = -2.6x + 2.6x + 2x2 + -2x2 Combine like terms: -2.6x + 2.6x = 0.0 4.08 + 2.6x + -2x2 = 0.0 + 2x2 + -2x2 4.08 + 2.6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 4.08 + 2.6x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.04 + -1.3x + x2 = 0 Move the constant term to the right: Add '2.04' to each side of the equation. -2.04 + -1.3x + 2.04 + x2 = 0 + 2.04 Reorder the terms: -2.04 + 2.04 + -1.3x + x2 = 0 + 2.04 Combine like terms: -2.04 + 2.04 = 0.00 0.00 + -1.3x + x2 = 0 + 2.04 -1.3x + x2 = 0 + 2.04 Combine like terms: 0 + 2.04 = 2.04 -1.3x + x2 = 2.04 The x term is -1.3x. Take half its coefficient (-0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. -1.3x + 0.4225 + x2 = 2.04 + 0.4225 Reorder the terms: 0.4225 + -1.3x + x2 = 2.04 + 0.4225 Combine like terms: 2.04 + 0.4225 = 2.4625 0.4225 + -1.3x + x2 = 2.4625 Factor a perfect square on the left side: (x + -0.65)(x + -0.65) = 2.4625 Calculate the square root of the right side: 1.569235483 Break this problem into two subproblems by setting (x + -0.65) equal to 1.569235483 and -1.569235483.Subproblem 1
x + -0.65 = 1.569235483 Simplifying x + -0.65 = 1.569235483 Reorder the terms: -0.65 + x = 1.569235483 Solving -0.65 + x = 1.569235483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = 1.569235483 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = 1.569235483 + 0.65 x = 1.569235483 + 0.65 Combine like terms: 1.569235483 + 0.65 = 2.219235483 x = 2.219235483 Simplifying x = 2.219235483Subproblem 2
x + -0.65 = -1.569235483 Simplifying x + -0.65 = -1.569235483 Reorder the terms: -0.65 + x = -1.569235483 Solving -0.65 + x = -1.569235483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = -1.569235483 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = -1.569235483 + 0.65 x = -1.569235483 + 0.65 Combine like terms: -1.569235483 + 0.65 = -0.919235483 x = -0.919235483 Simplifying x = -0.919235483Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.219235483, -0.919235483}
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