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Simplifying 4.9x2 + 10x + -90 = 0 Reorder the terms: -90 + 10x + 4.9x2 = 0 Solving -90 + 10x + 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'. -18.36734694 + 2.040816327x + x2 = 0 Move the constant term to the right: Add '18.36734694' to each side of the equation. -18.36734694 + 2.040816327x + 18.36734694 + x2 = 0 + 18.36734694 Reorder the terms: -18.36734694 + 18.36734694 + 2.040816327x + x2 = 0 + 18.36734694 Combine like terms: -18.36734694 + 18.36734694 = 0.00000000 0.00000000 + 2.040816327x + x2 = 0 + 18.36734694 2.040816327x + x2 = 0 + 18.36734694 Combine like terms: 0 + 18.36734694 = 18.36734694 2.040816327x + x2 = 18.36734694 The x term is 2.040816327x. Take half its coefficient (1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. 2.040816327x + 1.041232821 + x2 = 18.36734694 + 1.041232821 Reorder the terms: 1.041232821 + 2.040816327x + x2 = 18.36734694 + 1.041232821 Combine like terms: 18.36734694 + 1.041232821 = 19.408579761 1.041232821 + 2.040816327x + x2 = 19.408579761 Factor a perfect square on the left side: (x + 1.020408164)(x + 1.020408164) = 19.408579761 Calculate the square root of the right side: 4.405516969 Break this problem into two subproblems by setting (x + 1.020408164) equal to 4.405516969 and -4.405516969.Subproblem 1
x + 1.020408164 = 4.405516969 Simplifying x + 1.020408164 = 4.405516969 Reorder the terms: 1.020408164 + x = 4.405516969 Solving 1.020408164 + x = 4.405516969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + x = 4.405516969 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = 4.405516969 + -1.020408164 x = 4.405516969 + -1.020408164 Combine like terms: 4.405516969 + -1.020408164 = 3.385108805 x = 3.385108805 Simplifying x = 3.385108805Subproblem 2
x + 1.020408164 = -4.405516969 Simplifying x + 1.020408164 = -4.405516969 Reorder the terms: 1.020408164 + x = -4.405516969 Solving 1.020408164 + x = -4.405516969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + x = -4.405516969 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = -4.405516969 + -1.020408164 x = -4.405516969 + -1.020408164 Combine like terms: -4.405516969 + -1.020408164 = -5.425925133 x = -5.425925133 Simplifying x = -5.425925133Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.385108805, -5.425925133}
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