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Simplifying 5x2 + -51x + -2000 = 0 Reorder the terms: -2000 + -51x + 5x2 = 0 Solving -2000 + -51x + 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'. -400 + -10.2x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -10.2x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -10.2x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -10.2x + x2 = 0 + 400 -10.2x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -10.2x + x2 = 400 The x term is -10.2x. Take half its coefficient (-5.1). Square it (26.01) and add it to both sides. Add '26.01' to each side of the equation. -10.2x + 26.01 + x2 = 400 + 26.01 Reorder the terms: 26.01 + -10.2x + x2 = 400 + 26.01 Combine like terms: 400 + 26.01 = 426.01 26.01 + -10.2x + x2 = 426.01 Factor a perfect square on the left side: (x + -5.1)(x + -5.1) = 426.01 Calculate the square root of the right side: 20.64000969 Break this problem into two subproblems by setting (x + -5.1) equal to 20.64000969 and -20.64000969.Subproblem 1
x + -5.1 = 20.64000969 Simplifying x + -5.1 = 20.64000969 Reorder the terms: -5.1 + x = 20.64000969 Solving -5.1 + x = 20.64000969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + x = 20.64000969 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + x = 20.64000969 + 5.1 x = 20.64000969 + 5.1 Combine like terms: 20.64000969 + 5.1 = 25.74000969 x = 25.74000969 Simplifying x = 25.74000969Subproblem 2
x + -5.1 = -20.64000969 Simplifying x + -5.1 = -20.64000969 Reorder the terms: -5.1 + x = -20.64000969 Solving -5.1 + x = -20.64000969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + x = -20.64000969 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + x = -20.64000969 + 5.1 x = -20.64000969 + 5.1 Combine like terms: -20.64000969 + 5.1 = -15.54000969 x = -15.54000969 Simplifying x = -15.54000969Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.74000969, -15.54000969}
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