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Simplifying -0.05x2 + 2.1x + 6.3 = 0 Reorder the terms: 6.3 + 2.1x + -0.05x2 = 0 Solving 6.3 + 2.1x + -0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -126 + -42x + x2 = 0 Move the constant term to the right: Add '126' to each side of the equation. -126 + -42x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + -42x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + -42x + x2 = 0 + 126 -42x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 -42x + x2 = 126 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = 126 + 441 Reorder the terms: 441 + -42x + x2 = 126 + 441 Combine like terms: 126 + 441 = 567 441 + -42x + x2 = 567 Factor a perfect square on the left side: (x + -21)(x + -21) = 567 Calculate the square root of the right side: 23.8117618 Break this problem into two subproblems by setting (x + -21) equal to 23.8117618 and -23.8117618.Subproblem 1
x + -21 = 23.8117618 Simplifying x + -21 = 23.8117618 Reorder the terms: -21 + x = 23.8117618 Solving -21 + x = 23.8117618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 23.8117618 + 21 Combine like terms: -21 + 21 = 0 0 + x = 23.8117618 + 21 x = 23.8117618 + 21 Combine like terms: 23.8117618 + 21 = 44.8117618 x = 44.8117618 Simplifying x = 44.8117618Subproblem 2
x + -21 = -23.8117618 Simplifying x + -21 = -23.8117618 Reorder the terms: -21 + x = -23.8117618 Solving -21 + x = -23.8117618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -23.8117618 + 21 Combine like terms: -21 + 21 = 0 0 + x = -23.8117618 + 21 x = -23.8117618 + 21 Combine like terms: -23.8117618 + 21 = -2.8117618 x = -2.8117618 Simplifying x = -2.8117618Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.8117618, -2.8117618}
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