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Simplifying 5x2 + -42x + -4 = 0 Reorder the terms: -4 + -42x + 5x2 = 0 Solving -4 + -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'. -0.8 + -8.4x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -8.4x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -8.4x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -8.4x + x2 = 0 + 0.8 -8.4x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -8.4x + x2 = 0.8 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 = 0.8 + 17.64 Reorder the terms: 17.64 + -8.4x + x2 = 0.8 + 17.64 Combine like terms: 0.8 + 17.64 = 18.44 17.64 + -8.4x + x2 = 18.44 Factor a perfect square on the left side: (x + -4.2)(x + -4.2) = 18.44 Calculate the square root of the right side: 4.294182111 Break this problem into two subproblems by setting (x + -4.2) equal to 4.294182111 and -4.294182111.Subproblem 1
x + -4.2 = 4.294182111 Simplifying x + -4.2 = 4.294182111 Reorder the terms: -4.2 + x = 4.294182111 Solving -4.2 + x = 4.294182111 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 = 4.294182111 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + x = 4.294182111 + 4.2 x = 4.294182111 + 4.2 Combine like terms: 4.294182111 + 4.2 = 8.494182111 x = 8.494182111 Simplifying x = 8.494182111Subproblem 2
x + -4.2 = -4.294182111 Simplifying x + -4.2 = -4.294182111 Reorder the terms: -4.2 + x = -4.294182111 Solving -4.2 + x = -4.294182111 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 = -4.294182111 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + x = -4.294182111 + 4.2 x = -4.294182111 + 4.2 Combine like terms: -4.294182111 + 4.2 = -0.094182111 x = -0.094182111 Simplifying x = -0.094182111Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.494182111, -0.094182111}
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