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Simplifying 5x2 + -20x + 2 = 35 Reorder the terms: 2 + -20x + 5x2 = 35 Solving 2 + -20x + 5x2 = 35 Solving for variable 'x'. Reorder the terms: 2 + -35 + -20x + 5x2 = 35 + -35 Combine like terms: 2 + -35 = -33 -33 + -20x + 5x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -33 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.6 + -4x + x2 = 0 Move the constant term to the right: Add '6.6' to each side of the equation. -6.6 + -4x + 6.6 + x2 = 0 + 6.6 Reorder the terms: -6.6 + 6.6 + -4x + x2 = 0 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + -4x + x2 = 0 + 6.6 -4x + x2 = 0 + 6.6 Combine like terms: 0 + 6.6 = 6.6 -4x + x2 = 6.6 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 6.6 + 4 Reorder the terms: 4 + -4x + x2 = 6.6 + 4 Combine like terms: 6.6 + 4 = 10.6 4 + -4x + x2 = 10.6 Factor a perfect square on the left side: (x + -2)(x + -2) = 10.6 Calculate the square root of the right side: 3.255764119 Break this problem into two subproblems by setting (x + -2) equal to 3.255764119 and -3.255764119.Subproblem 1
x + -2 = 3.255764119 Simplifying x + -2 = 3.255764119 Reorder the terms: -2 + x = 3.255764119 Solving -2 + x = 3.255764119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.255764119 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.255764119 + 2 x = 3.255764119 + 2 Combine like terms: 3.255764119 + 2 = 5.255764119 x = 5.255764119 Simplifying x = 5.255764119Subproblem 2
x + -2 = -3.255764119 Simplifying x + -2 = -3.255764119 Reorder the terms: -2 + x = -3.255764119 Solving -2 + x = -3.255764119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.255764119 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.255764119 + 2 x = -3.255764119 + 2 Combine like terms: -3.255764119 + 2 = -1.255764119 x = -1.255764119 Simplifying x = -1.255764119Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.255764119, -1.255764119}
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