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Simplifying 4.9x2 + -2.6x + -8.8 = 0 Reorder the terms: -8.8 + -2.6x + 4.9x2 = 0 Solving -8.8 + -2.6x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.795918367 + -0.5306122449x + x2 = 0 Move the constant term to the right: Add '1.795918367' to each side of the equation. -1.795918367 + -0.5306122449x + 1.795918367 + x2 = 0 + 1.795918367 Reorder the terms: -1.795918367 + 1.795918367 + -0.5306122449x + x2 = 0 + 1.795918367 Combine like terms: -1.795918367 + 1.795918367 = 0.000000000 0.000000000 + -0.5306122449x + x2 = 0 + 1.795918367 -0.5306122449x + x2 = 0 + 1.795918367 Combine like terms: 0 + 1.795918367 = 1.795918367 -0.5306122449x + x2 = 1.795918367 The x term is -0.5306122449x. Take half its coefficient (-0.2653061225). Square it (0.07038733864) and add it to both sides. Add '0.07038733864' to each side of the equation. -0.5306122449x + 0.07038733864 + x2 = 1.795918367 + 0.07038733864 Reorder the terms: 0.07038733864 + -0.5306122449x + x2 = 1.795918367 + 0.07038733864 Combine like terms: 1.795918367 + 0.07038733864 = 1.86630570564 0.07038733864 + -0.5306122449x + x2 = 1.86630570564 Factor a perfect square on the left side: (x + -0.2653061225)(x + -0.2653061225) = 1.86630570564 Calculate the square root of the right side: 1.366127998 Break this problem into two subproblems by setting (x + -0.2653061225) equal to 1.366127998 and -1.366127998.Subproblem 1
x + -0.2653061225 = 1.366127998 Simplifying x + -0.2653061225 = 1.366127998 Reorder the terms: -0.2653061225 + x = 1.366127998 Solving -0.2653061225 + x = 1.366127998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2653061225' to each side of the equation. -0.2653061225 + 0.2653061225 + x = 1.366127998 + 0.2653061225 Combine like terms: -0.2653061225 + 0.2653061225 = 0.0000000000 0.0000000000 + x = 1.366127998 + 0.2653061225 x = 1.366127998 + 0.2653061225 Combine like terms: 1.366127998 + 0.2653061225 = 1.6314341205 x = 1.6314341205 Simplifying x = 1.6314341205Subproblem 2
x + -0.2653061225 = -1.366127998 Simplifying x + -0.2653061225 = -1.366127998 Reorder the terms: -0.2653061225 + x = -1.366127998 Solving -0.2653061225 + x = -1.366127998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2653061225' to each side of the equation. -0.2653061225 + 0.2653061225 + x = -1.366127998 + 0.2653061225 Combine like terms: -0.2653061225 + 0.2653061225 = 0.0000000000 0.0000000000 + x = -1.366127998 + 0.2653061225 x = -1.366127998 + 0.2653061225 Combine like terms: -1.366127998 + 0.2653061225 = -1.1008218755 x = -1.1008218755 Simplifying x = -1.1008218755Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6314341205, -1.1008218755}
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