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Simplifying 0.3x2 + -2.4x + 2.1 = 0 Reorder the terms: 2.1 + -2.4x + 0.3x2 = 0 Solving 2.1 + -2.4x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 7 + -8x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -8x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -8x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8x + x2 = 0 + -7 -8x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -8x + x2 = -7 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -7 + 16 Reorder the terms: 16 + -8x + x2 = -7 + 16 Combine like terms: -7 + 16 = 9 16 + -8x + x2 = 9 Factor a perfect square on the left side: (x + -4)(x + -4) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + -4) equal to 3 and -3.Subproblem 1
x + -4 = 3 Simplifying x + -4 = 3 Reorder the terms: -4 + x = 3 Solving -4 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3 + 4 x = 3 + 4 Combine like terms: 3 + 4 = 7 x = 7 Simplifying x = 7Subproblem 2
x + -4 = -3 Simplifying x + -4 = -3 Reorder the terms: -4 + x = -3 Solving -4 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3 + 4 x = -3 + 4 Combine like terms: -3 + 4 = 1 x = 1 Simplifying x = 1Solution
The solution to the problem is based on the solutions from the subproblems. x = {7, 1}
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