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Simplifying 15x2 + -3x = 64 Reorder the terms: -3x + 15x2 = 64 Solving -3x + 15x2 = 64 Solving for variable 'x'. Reorder the terms: -64 + -3x + 15x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + -3x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -4.266666667 + -0.2x + x2 = 0 Move the constant term to the right: Add '4.266666667' to each side of the equation. -4.266666667 + -0.2x + 4.266666667 + x2 = 0 + 4.266666667 Reorder the terms: -4.266666667 + 4.266666667 + -0.2x + x2 = 0 + 4.266666667 Combine like terms: -4.266666667 + 4.266666667 = 0.000000000 0.000000000 + -0.2x + x2 = 0 + 4.266666667 -0.2x + x2 = 0 + 4.266666667 Combine like terms: 0 + 4.266666667 = 4.266666667 -0.2x + x2 = 4.266666667 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 4.266666667 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 4.266666667 + 0.01 Combine like terms: 4.266666667 + 0.01 = 4.276666667 0.01 + -0.2x + x2 = 4.276666667 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 4.276666667 Calculate the square root of the right side: 2.068010316 Break this problem into two subproblems by setting (x + -0.1) equal to 2.068010316 and -2.068010316.Subproblem 1
x + -0.1 = 2.068010316 Simplifying x + -0.1 = 2.068010316 Reorder the terms: -0.1 + x = 2.068010316 Solving -0.1 + x = 2.068010316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 2.068010316 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 2.068010316 + 0.1 x = 2.068010316 + 0.1 Combine like terms: 2.068010316 + 0.1 = 2.168010316 x = 2.168010316 Simplifying x = 2.168010316Subproblem 2
x + -0.1 = -2.068010316 Simplifying x + -0.1 = -2.068010316 Reorder the terms: -0.1 + x = -2.068010316 Solving -0.1 + x = -2.068010316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -2.068010316 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -2.068010316 + 0.1 x = -2.068010316 + 0.1 Combine like terms: -2.068010316 + 0.1 = -1.968010316 x = -1.968010316 Simplifying x = -1.968010316Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.168010316, -1.968010316}
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