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Simplifying 5x2 + 21x = 55 Reorder the terms: 21x + 5x2 = 55 Solving 21x + 5x2 = 55 Solving for variable 'x'. Reorder the terms: -55 + 21x + 5x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + 21x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11 + 4.2x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 4.2x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 4.2x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 4.2x + x2 = 0 + 11 4.2x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 4.2x + x2 = 11 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 = 11 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = 11 + 4.41 Combine like terms: 11 + 4.41 = 15.41 4.41 + 4.2x + x2 = 15.41 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 15.41 Calculate the square root of the right side: 3.925557285 Break this problem into two subproblems by setting (x + 2.1) equal to 3.925557285 and -3.925557285.Subproblem 1
x + 2.1 = 3.925557285 Simplifying x + 2.1 = 3.925557285 Reorder the terms: 2.1 + x = 3.925557285 Solving 2.1 + x = 3.925557285 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 = 3.925557285 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 3.925557285 + -2.1 x = 3.925557285 + -2.1 Combine like terms: 3.925557285 + -2.1 = 1.825557285 x = 1.825557285 Simplifying x = 1.825557285Subproblem 2
x + 2.1 = -3.925557285 Simplifying x + 2.1 = -3.925557285 Reorder the terms: 2.1 + x = -3.925557285 Solving 2.1 + x = -3.925557285 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 = -3.925557285 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -3.925557285 + -2.1 x = -3.925557285 + -2.1 Combine like terms: -3.925557285 + -2.1 = -6.025557285 x = -6.025557285 Simplifying x = -6.025557285Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.825557285, -6.025557285}
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