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Simplifying x2 + -2.8x = 9 Reorder the terms: -2.8x + x2 = 9 Solving -2.8x + x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -2.8x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -2.8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -2.8x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -2.8x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2.8x + x2 = 0 + 9 -2.8x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2.8x + x2 = 9 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = 9 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 9 + 1.96 Combine like terms: 9 + 1.96 = 10.96 1.96 + -2.8x + x2 = 10.96 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 10.96 Calculate the square root of the right side: 3.310589071 Break this problem into two subproblems by setting (x + -1.4) equal to 3.310589071 and -3.310589071.Subproblem 1
x + -1.4 = 3.310589071 Simplifying x + -1.4 = 3.310589071 Reorder the terms: -1.4 + x = 3.310589071 Solving -1.4 + x = 3.310589071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 3.310589071 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 3.310589071 + 1.4 x = 3.310589071 + 1.4 Combine like terms: 3.310589071 + 1.4 = 4.710589071 x = 4.710589071 Simplifying x = 4.710589071Subproblem 2
x + -1.4 = -3.310589071 Simplifying x + -1.4 = -3.310589071 Reorder the terms: -1.4 + x = -3.310589071 Solving -1.4 + x = -3.310589071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -3.310589071 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -3.310589071 + 1.4 x = -3.310589071 + 1.4 Combine like terms: -3.310589071 + 1.4 = -1.910589071 x = -1.910589071 Simplifying x = -1.910589071Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.710589071, -1.910589071}
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