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Simplifying 5x2 + -6x + -16 = 0 Reorder the terms: -16 + -6x + 5x2 = 0 Solving -16 + -6x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + -1.2x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -1.2x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -1.2x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -1.2x + x2 = 0 + 3.2 -1.2x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -1.2x + x2 = 3.2 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 3.2 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 3.2 + 0.36 Combine like terms: 3.2 + 0.36 = 3.56 0.36 + -1.2x + x2 = 3.56 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 3.56 Calculate the square root of the right side: 1.886796226 Break this problem into two subproblems by setting (x + -0.6) equal to 1.886796226 and -1.886796226.Subproblem 1
x + -0.6 = 1.886796226 Simplifying x + -0.6 = 1.886796226 Reorder the terms: -0.6 + x = 1.886796226 Solving -0.6 + x = 1.886796226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.886796226 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.886796226 + 0.6 x = 1.886796226 + 0.6 Combine like terms: 1.886796226 + 0.6 = 2.486796226 x = 2.486796226 Simplifying x = 2.486796226Subproblem 2
x + -0.6 = -1.886796226 Simplifying x + -0.6 = -1.886796226 Reorder the terms: -0.6 + x = -1.886796226 Solving -0.6 + x = -1.886796226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.886796226 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.886796226 + 0.6 x = -1.886796226 + 0.6 Combine like terms: -1.886796226 + 0.6 = -1.286796226 x = -1.286796226 Simplifying x = -1.286796226Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.486796226, -1.286796226}
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