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Simplifying 4x2 + -27x + 42 = 0 Reorder the terms: 42 + -27x + 4x2 = 0 Solving 42 + -27x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 10.5 + -6.75x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -6.75x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -6.75x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -6.75x + x2 = 0 + -10.5 -6.75x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -6.75x + x2 = -10.5 The x term is -6.75x. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75x + 11.390625 + x2 = -10.5 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = -10.5 + 11.390625 Combine like terms: -10.5 + 11.390625 = 0.890625 11.390625 + -6.75x + x2 = 0.890625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + -3.375) equal to 0.943729304 and -0.943729304.Subproblem 1
x + -3.375 = 0.943729304 Simplifying x + -3.375 = 0.943729304 Reorder the terms: -3.375 + x = 0.943729304 Solving -3.375 + x = 0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 0.943729304 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 0.943729304 + 3.375 x = 0.943729304 + 3.375 Combine like terms: 0.943729304 + 3.375 = 4.318729304 x = 4.318729304 Simplifying x = 4.318729304Subproblem 2
x + -3.375 = -0.943729304 Simplifying x + -3.375 = -0.943729304 Reorder the terms: -3.375 + x = -0.943729304 Solving -3.375 + x = -0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -0.943729304 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -0.943729304 + 3.375 x = -0.943729304 + 3.375 Combine like terms: -0.943729304 + 3.375 = 2.431270696 x = 2.431270696 Simplifying x = 2.431270696Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.318729304, 2.431270696}
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