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Simplifying 5x2 + -21x = 18 Reorder the terms: -21x + 5x2 = 18 Solving -21x + 5x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + -21x + 5x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -21x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + -4.2x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -4.2x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -4.2x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -4.2x + x2 = 0 + 3.6 -4.2x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -4.2x + x2 = 3.6 The x term is -4.2x. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2x + 4.41 + x2 = 3.6 + 4.41 Reorder the terms: 4.41 + -4.2x + x2 = 3.6 + 4.41 Combine like terms: 3.6 + 4.41 = 8.01 4.41 + -4.2x + x2 = 8.01 Factor a perfect square on the left side: (x + -2.1)(x + -2.1) = 8.01 Calculate the square root of the right side: 2.83019434 Break this problem into two subproblems by setting (x + -2.1) equal to 2.83019434 and -2.83019434.Subproblem 1
x + -2.1 = 2.83019434 Simplifying x + -2.1 = 2.83019434 Reorder the terms: -2.1 + x = 2.83019434 Solving -2.1 + x = 2.83019434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = 2.83019434 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = 2.83019434 + 2.1 x = 2.83019434 + 2.1 Combine like terms: 2.83019434 + 2.1 = 4.93019434 x = 4.93019434 Simplifying x = 4.93019434Subproblem 2
x + -2.1 = -2.83019434 Simplifying x + -2.1 = -2.83019434 Reorder the terms: -2.1 + x = -2.83019434 Solving -2.1 + x = -2.83019434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = -2.83019434 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = -2.83019434 + 2.1 x = -2.83019434 + 2.1 Combine like terms: -2.83019434 + 2.1 = -0.73019434 x = -0.73019434 Simplifying x = -0.73019434Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.93019434, -0.73019434}
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