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Simplifying x2 + -2.8x + 1.96 = 349.69 Reorder the terms: 1.96 + -2.8x + x2 = 349.69 Solving 1.96 + -2.8x + x2 = 349.69 Solving for variable 'x'. Reorder the terms: 1.96 + -349.69 + -2.8x + x2 = 349.69 + -349.69 Combine like terms: 1.96 + -349.69 = -347.73 -347.73 + -2.8x + x2 = 349.69 + -349.69 Combine like terms: 349.69 + -349.69 = 0.00 -347.73 + -2.8x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '347.73' to each side of the equation. -347.73 + -2.8x + 347.73 + x2 = 0.00 + 347.73 Reorder the terms: -347.73 + 347.73 + -2.8x + x2 = 0.00 + 347.73 Combine like terms: -347.73 + 347.73 = 0.00 0.00 + -2.8x + x2 = 0.00 + 347.73 -2.8x + x2 = 0.00 + 347.73 Combine like terms: 0.00 + 347.73 = 347.73 -2.8x + x2 = 347.73 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 = 347.73 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 347.73 + 1.96 Combine like terms: 347.73 + 1.96 = 349.69 1.96 + -2.8x + x2 = 349.69 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 349.69 Calculate the square root of the right side: 18.7 Break this problem into two subproblems by setting (x + -1.4) equal to 18.7 and -18.7.Subproblem 1
x + -1.4 = 18.7 Simplifying x + -1.4 = 18.7 Reorder the terms: -1.4 + x = 18.7 Solving -1.4 + x = 18.7 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 = 18.7 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 18.7 + 1.4 x = 18.7 + 1.4 Combine like terms: 18.7 + 1.4 = 20.1 x = 20.1 Simplifying x = 20.1Subproblem 2
x + -1.4 = -18.7 Simplifying x + -1.4 = -18.7 Reorder the terms: -1.4 + x = -18.7 Solving -1.4 + x = -18.7 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 = -18.7 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -18.7 + 1.4 x = -18.7 + 1.4 Combine like terms: -18.7 + 1.4 = -17.3 x = -17.3 Simplifying x = -17.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.1, -17.3}
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