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Simplifying -0.01x2 + 0.6x + 6.4 = 0 Reorder the terms: 6.4 + 0.6x + -0.01x2 = 0 Solving 6.4 + 0.6x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -640 + -60x + x2 = 0 Move the constant term to the right: Add '640' to each side of the equation. -640 + -60x + 640 + x2 = 0 + 640 Reorder the terms: -640 + 640 + -60x + x2 = 0 + 640 Combine like terms: -640 + 640 = 0 0 + -60x + x2 = 0 + 640 -60x + x2 = 0 + 640 Combine like terms: 0 + 640 = 640 -60x + x2 = 640 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = 640 + 900 Reorder the terms: 900 + -60x + x2 = 640 + 900 Combine like terms: 640 + 900 = 1540 900 + -60x + x2 = 1540 Factor a perfect square on the left side: (x + -30)(x + -30) = 1540 Calculate the square root of the right side: 39.242833741 Break this problem into two subproblems by setting (x + -30) equal to 39.242833741 and -39.242833741.Subproblem 1
x + -30 = 39.242833741 Simplifying x + -30 = 39.242833741 Reorder the terms: -30 + x = 39.242833741 Solving -30 + x = 39.242833741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 39.242833741 + 30 Combine like terms: -30 + 30 = 0 0 + x = 39.242833741 + 30 x = 39.242833741 + 30 Combine like terms: 39.242833741 + 30 = 69.242833741 x = 69.242833741 Simplifying x = 69.242833741Subproblem 2
x + -30 = -39.242833741 Simplifying x + -30 = -39.242833741 Reorder the terms: -30 + x = -39.242833741 Solving -30 + x = -39.242833741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -39.242833741 + 30 Combine like terms: -30 + 30 = 0 0 + x = -39.242833741 + 30 x = -39.242833741 + 30 Combine like terms: -39.242833741 + 30 = -9.242833741 x = -9.242833741 Simplifying x = -9.242833741Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.242833741, -9.242833741}
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