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Simplifying 5x2 + -2x + -89 = 0 Reorder the terms: -89 + -2x + 5x2 = 0 Solving -89 + -2x + 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'. -17.8 + -0.4x + x2 = 0 Move the constant term to the right: Add '17.8' to each side of the equation. -17.8 + -0.4x + 17.8 + x2 = 0 + 17.8 Reorder the terms: -17.8 + 17.8 + -0.4x + x2 = 0 + 17.8 Combine like terms: -17.8 + 17.8 = 0.0 0.0 + -0.4x + x2 = 0 + 17.8 -0.4x + x2 = 0 + 17.8 Combine like terms: 0 + 17.8 = 17.8 -0.4x + x2 = 17.8 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 17.8 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 17.8 + 0.04 Combine like terms: 17.8 + 0.04 = 17.84 0.04 + -0.4x + x2 = 17.84 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 17.84 Calculate the square root of the right side: 4.223742416 Break this problem into two subproblems by setting (x + -0.2) equal to 4.223742416 and -4.223742416.Subproblem 1
x + -0.2 = 4.223742416 Simplifying x + -0.2 = 4.223742416 Reorder the terms: -0.2 + x = 4.223742416 Solving -0.2 + x = 4.223742416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 4.223742416 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 4.223742416 + 0.2 x = 4.223742416 + 0.2 Combine like terms: 4.223742416 + 0.2 = 4.423742416 x = 4.423742416 Simplifying x = 4.423742416Subproblem 2
x + -0.2 = -4.223742416 Simplifying x + -0.2 = -4.223742416 Reorder the terms: -0.2 + x = -4.223742416 Solving -0.2 + x = -4.223742416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -4.223742416 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -4.223742416 + 0.2 x = -4.223742416 + 0.2 Combine like terms: -4.223742416 + 0.2 = -4.023742416 x = -4.023742416 Simplifying x = -4.023742416Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.423742416, -4.023742416}
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