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Simplifying 20x2 + -21x + 4.5 = 0 Reorder the terms: 4.5 + -21x + 20x2 = 0 Solving 4.5 + -21x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.225 + -1.05x + x2 = 0 Move the constant term to the right: Add '-0.225' to each side of the equation. 0.225 + -1.05x + -0.225 + x2 = 0 + -0.225 Reorder the terms: 0.225 + -0.225 + -1.05x + x2 = 0 + -0.225 Combine like terms: 0.225 + -0.225 = 0.000 0.000 + -1.05x + x2 = 0 + -0.225 -1.05x + x2 = 0 + -0.225 Combine like terms: 0 + -0.225 = -0.225 -1.05x + x2 = -0.225 The x term is -1.05x. Take half its coefficient (-0.525). Square it (0.275625) and add it to both sides. Add '0.275625' to each side of the equation. -1.05x + 0.275625 + x2 = -0.225 + 0.275625 Reorder the terms: 0.275625 + -1.05x + x2 = -0.225 + 0.275625 Combine like terms: -0.225 + 0.275625 = 0.050625 0.275625 + -1.05x + x2 = 0.050625 Factor a perfect square on the left side: (x + -0.525)(x + -0.525) = 0.050625 Calculate the square root of the right side: 0.225 Break this problem into two subproblems by setting (x + -0.525) equal to 0.225 and -0.225.Subproblem 1
x + -0.525 = 0.225 Simplifying x + -0.525 = 0.225 Reorder the terms: -0.525 + x = 0.225 Solving -0.525 + x = 0.225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.525' to each side of the equation. -0.525 + 0.525 + x = 0.225 + 0.525 Combine like terms: -0.525 + 0.525 = 0.000 0.000 + x = 0.225 + 0.525 x = 0.225 + 0.525 Combine like terms: 0.225 + 0.525 = 0.75 x = 0.75 Simplifying x = 0.75Subproblem 2
x + -0.525 = -0.225 Simplifying x + -0.525 = -0.225 Reorder the terms: -0.525 + x = -0.225 Solving -0.525 + x = -0.225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.525' to each side of the equation. -0.525 + 0.525 + x = -0.225 + 0.525 Combine like terms: -0.525 + 0.525 = 0.000 0.000 + x = -0.225 + 0.525 x = -0.225 + 0.525 Combine like terms: -0.225 + 0.525 = 0.3 x = 0.3 Simplifying x = 0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.75, 0.3}
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