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Simplifying 4.9x2 + 2.3x + -180 = 0 Reorder the terms: -180 + 2.3x + 4.9x2 = 0 Solving -180 + 2.3x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -36.73469388 + 0.4693877551x + x2 = 0 Move the constant term to the right: Add '36.73469388' to each side of the equation. -36.73469388 + 0.4693877551x + 36.73469388 + x2 = 0 + 36.73469388 Reorder the terms: -36.73469388 + 36.73469388 + 0.4693877551x + x2 = 0 + 36.73469388 Combine like terms: -36.73469388 + 36.73469388 = 0.00000000 0.00000000 + 0.4693877551x + x2 = 0 + 36.73469388 0.4693877551x + x2 = 0 + 36.73469388 Combine like terms: 0 + 36.73469388 = 36.73469388 0.4693877551x + x2 = 36.73469388 The x term is 0.4693877551x. Take half its coefficient (0.2346938776). Square it (0.05508121618) and add it to both sides. Add '0.05508121618' to each side of the equation. 0.4693877551x + 0.05508121618 + x2 = 36.73469388 + 0.05508121618 Reorder the terms: 0.05508121618 + 0.4693877551x + x2 = 36.73469388 + 0.05508121618 Combine like terms: 36.73469388 + 0.05508121618 = 36.78977509618 0.05508121618 + 0.4693877551x + x2 = 36.78977509618 Factor a perfect square on the left side: (x + 0.2346938776)(x + 0.2346938776) = 36.78977509618 Calculate the square root of the right side: 6.065457534 Break this problem into two subproblems by setting (x + 0.2346938776) equal to 6.065457534 and -6.065457534.Subproblem 1
x + 0.2346938776 = 6.065457534 Simplifying x + 0.2346938776 = 6.065457534 Reorder the terms: 0.2346938776 + x = 6.065457534 Solving 0.2346938776 + x = 6.065457534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2346938776' to each side of the equation. 0.2346938776 + -0.2346938776 + x = 6.065457534 + -0.2346938776 Combine like terms: 0.2346938776 + -0.2346938776 = 0.0000000000 0.0000000000 + x = 6.065457534 + -0.2346938776 x = 6.065457534 + -0.2346938776 Combine like terms: 6.065457534 + -0.2346938776 = 5.8307636564 x = 5.8307636564 Simplifying x = 5.8307636564Subproblem 2
x + 0.2346938776 = -6.065457534 Simplifying x + 0.2346938776 = -6.065457534 Reorder the terms: 0.2346938776 + x = -6.065457534 Solving 0.2346938776 + x = -6.065457534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2346938776' to each side of the equation. 0.2346938776 + -0.2346938776 + x = -6.065457534 + -0.2346938776 Combine like terms: 0.2346938776 + -0.2346938776 = 0.0000000000 0.0000000000 + x = -6.065457534 + -0.2346938776 x = -6.065457534 + -0.2346938776 Combine like terms: -6.065457534 + -0.2346938776 = -6.3001514116 x = -6.3001514116 Simplifying x = -6.3001514116Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.8307636564, -6.3001514116}
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