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Simplifying 5x2 + -42x + 8 = 0 Reorder the terms: 8 + -42x + 5x2 = 0 Solving 8 + -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'. 1.6 + -8.4x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -8.4x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -8.4x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -8.4x + x2 = 0 + -1.6 -8.4x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -8.4x + x2 = -1.6 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 = -1.6 + 17.64 Reorder the terms: 17.64 + -8.4x + x2 = -1.6 + 17.64 Combine like terms: -1.6 + 17.64 = 16.04 17.64 + -8.4x + x2 = 16.04 Factor a perfect square on the left side: (x + -4.2)(x + -4.2) = 16.04 Calculate the square root of the right side: 4.004996879 Break this problem into two subproblems by setting (x + -4.2) equal to 4.004996879 and -4.004996879.Subproblem 1
x + -4.2 = 4.004996879 Simplifying x + -4.2 = 4.004996879 Reorder the terms: -4.2 + x = 4.004996879 Solving -4.2 + x = 4.004996879 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 = 4.004996879 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + x = 4.004996879 + 4.2 x = 4.004996879 + 4.2 Combine like terms: 4.004996879 + 4.2 = 8.204996879 x = 8.204996879 Simplifying x = 8.204996879Subproblem 2
x + -4.2 = -4.004996879 Simplifying x + -4.2 = -4.004996879 Reorder the terms: -4.2 + x = -4.004996879 Solving -4.2 + x = -4.004996879 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 = -4.004996879 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + x = -4.004996879 + 4.2 x = -4.004996879 + 4.2 Combine like terms: -4.004996879 + 4.2 = 0.195003121 x = 0.195003121 Simplifying x = 0.195003121Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.204996879, 0.195003121}
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