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Simplifying 4.905x2 + -23.41x + -15 = 0 Reorder the terms: -15 + -23.41x + 4.905x2 = 0 Solving -15 + -23.41x + 4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -3.058103976 + -4.772680938x + x2 = 0 Move the constant term to the right: Add '3.058103976' to each side of the equation. -3.058103976 + -4.772680938x + 3.058103976 + x2 = 0 + 3.058103976 Reorder the terms: -3.058103976 + 3.058103976 + -4.772680938x + x2 = 0 + 3.058103976 Combine like terms: -3.058103976 + 3.058103976 = 0.000000000 0.000000000 + -4.772680938x + x2 = 0 + 3.058103976 -4.772680938x + x2 = 0 + 3.058103976 Combine like terms: 0 + 3.058103976 = 3.058103976 -4.772680938x + x2 = 3.058103976 The x term is -4.772680938x. Take half its coefficient (-2.386340469). Square it (5.694620834) and add it to both sides. Add '5.694620834' to each side of the equation. -4.772680938x + 5.694620834 + x2 = 3.058103976 + 5.694620834 Reorder the terms: 5.694620834 + -4.772680938x + x2 = 3.058103976 + 5.694620834 Combine like terms: 3.058103976 + 5.694620834 = 8.75272481 5.694620834 + -4.772680938x + x2 = 8.75272481 Factor a perfect square on the left side: (x + -2.386340469)(x + -2.386340469) = 8.75272481 Calculate the square root of the right side: 2.958500433 Break this problem into two subproblems by setting (x + -2.386340469) equal to 2.958500433 and -2.958500433.Subproblem 1
x + -2.386340469 = 2.958500433 Simplifying x + -2.386340469 = 2.958500433 Reorder the terms: -2.386340469 + x = 2.958500433 Solving -2.386340469 + x = 2.958500433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.386340469' to each side of the equation. -2.386340469 + 2.386340469 + x = 2.958500433 + 2.386340469 Combine like terms: -2.386340469 + 2.386340469 = 0.000000000 0.000000000 + x = 2.958500433 + 2.386340469 x = 2.958500433 + 2.386340469 Combine like terms: 2.958500433 + 2.386340469 = 5.344840902 x = 5.344840902 Simplifying x = 5.344840902Subproblem 2
x + -2.386340469 = -2.958500433 Simplifying x + -2.386340469 = -2.958500433 Reorder the terms: -2.386340469 + x = -2.958500433 Solving -2.386340469 + x = -2.958500433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.386340469' to each side of the equation. -2.386340469 + 2.386340469 + x = -2.958500433 + 2.386340469 Combine like terms: -2.386340469 + 2.386340469 = 0.000000000 0.000000000 + x = -2.958500433 + 2.386340469 x = -2.958500433 + 2.386340469 Combine like terms: -2.958500433 + 2.386340469 = -0.572159964 x = -0.572159964 Simplifying x = -0.572159964Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.344840902, -0.572159964}
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