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Simplifying 5x2 + -42x + 27 = 0 Reorder the terms: 27 + -42x + 5x2 = 0 Solving 27 + -42x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.4 + -8.4x + x2 = 0 Move the constant term to the right: Add '-5.4' to each side of the equation. 5.4 + -8.4x + -5.4 + x2 = 0 + -5.4 Reorder the terms: 5.4 + -5.4 + -8.4x + x2 = 0 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + -8.4x + x2 = 0 + -5.4 -8.4x + x2 = 0 + -5.4 Combine like terms: 0 + -5.4 = -5.4 -8.4x + x2 = -5.4 The x term is -8.4x. Take half its coefficient (-4.2). Square it (17.64) and add it to both sides. Add '17.64' to each side of the equation. -8.4x + 17.64 + x2 = -5.4 + 17.64 Reorder the terms: 17.64 + -8.4x + x2 = -5.4 + 17.64 Combine like terms: -5.4 + 17.64 = 12.24 17.64 + -8.4x + x2 = 12.24 Factor a perfect square on the left side: (x + -4.2)(x + -4.2) = 12.24 Calculate the square root of the right side: 3.498571137 Break this problem into two subproblems by setting (x + -4.2) equal to 3.498571137 and -3.498571137.Subproblem 1
x + -4.2 = 3.498571137 Simplifying x + -4.2 = 3.498571137 Reorder the terms: -4.2 + x = 3.498571137 Solving -4.2 + x = 3.498571137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.2' to each side of the equation. -4.2 + 4.2 + x = 3.498571137 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + x = 3.498571137 + 4.2 x = 3.498571137 + 4.2 Combine like terms: 3.498571137 + 4.2 = 7.698571137 x = 7.698571137 Simplifying x = 7.698571137Subproblem 2
x + -4.2 = -3.498571137 Simplifying x + -4.2 = -3.498571137 Reorder the terms: -4.2 + x = -3.498571137 Solving -4.2 + x = -3.498571137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.2' to each side of the equation. -4.2 + 4.2 + x = -3.498571137 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + x = -3.498571137 + 4.2 x = -3.498571137 + 4.2 Combine like terms: -3.498571137 + 4.2 = 0.701428863 x = 0.701428863 Simplifying x = 0.701428863Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.698571137, 0.701428863}
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