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Simplifying 8.4x2 + -234x + 1226 = 0 Reorder the terms: 1226 + -234x + 8.4x2 = 0 Solving 1226 + -234x + 8.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8.4 the coefficient of the squared term: Divide each side by '8.4'. 145.952381 + -27.85714286x + x2 = 0 Move the constant term to the right: Add '-145.952381' to each side of the equation. 145.952381 + -27.85714286x + -145.952381 + x2 = 0 + -145.952381 Reorder the terms: 145.952381 + -145.952381 + -27.85714286x + x2 = 0 + -145.952381 Combine like terms: 145.952381 + -145.952381 = 0.000000 0.000000 + -27.85714286x + x2 = 0 + -145.952381 -27.85714286x + x2 = 0 + -145.952381 Combine like terms: 0 + -145.952381 = -145.952381 -27.85714286x + x2 = -145.952381 The x term is -27.85714286x. Take half its coefficient (-13.92857143). Square it (194.0051021) and add it to both sides. Add '194.0051021' to each side of the equation. -27.85714286x + 194.0051021 + x2 = -145.952381 + 194.0051021 Reorder the terms: 194.0051021 + -27.85714286x + x2 = -145.952381 + 194.0051021 Combine like terms: -145.952381 + 194.0051021 = 48.0527211 194.0051021 + -27.85714286x + x2 = 48.0527211 Factor a perfect square on the left side: (x + -13.92857143)(x + -13.92857143) = 48.0527211 Calculate the square root of the right side: 6.932007004 Break this problem into two subproblems by setting (x + -13.92857143) equal to 6.932007004 and -6.932007004.Subproblem 1
x + -13.92857143 = 6.932007004 Simplifying x + -13.92857143 = 6.932007004 Reorder the terms: -13.92857143 + x = 6.932007004 Solving -13.92857143 + x = 6.932007004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.92857143' to each side of the equation. -13.92857143 + 13.92857143 + x = 6.932007004 + 13.92857143 Combine like terms: -13.92857143 + 13.92857143 = 0.00000000 0.00000000 + x = 6.932007004 + 13.92857143 x = 6.932007004 + 13.92857143 Combine like terms: 6.932007004 + 13.92857143 = 20.860578434 x = 20.860578434 Simplifying x = 20.860578434Subproblem 2
x + -13.92857143 = -6.932007004 Simplifying x + -13.92857143 = -6.932007004 Reorder the terms: -13.92857143 + x = -6.932007004 Solving -13.92857143 + x = -6.932007004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.92857143' to each side of the equation. -13.92857143 + 13.92857143 + x = -6.932007004 + 13.92857143 Combine like terms: -13.92857143 + 13.92857143 = 0.00000000 0.00000000 + x = -6.932007004 + 13.92857143 x = -6.932007004 + 13.92857143 Combine like terms: -6.932007004 + 13.92857143 = 6.996564426 x = 6.996564426 Simplifying x = 6.996564426Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.860578434, 6.996564426}
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