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Simplifying 10x2 + -16x + 3 = 0 Reorder the terms: 3 + -16x + 10x2 = 0 Solving 3 + -16x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.3 + -1.6x + x2 = 0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + -1.6x + -0.3 + x2 = 0 + -0.3 Reorder the terms: 0.3 + -0.3 + -1.6x + x2 = 0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + -1.6x + x2 = 0 + -0.3 -1.6x + x2 = 0 + -0.3 Combine like terms: 0 + -0.3 = -0.3 -1.6x + x2 = -0.3 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = -0.3 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = -0.3 + 0.64 Combine like terms: -0.3 + 0.64 = 0.34 0.64 + -1.6x + x2 = 0.34 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 0.34 Calculate the square root of the right side: 0.583095189 Break this problem into two subproblems by setting (x + -0.8) equal to 0.583095189 and -0.583095189.Subproblem 1
x + -0.8 = 0.583095189 Simplifying x + -0.8 = 0.583095189 Reorder the terms: -0.8 + x = 0.583095189 Solving -0.8 + x = 0.583095189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 0.583095189 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0.583095189 + 0.8 x = 0.583095189 + 0.8 Combine like terms: 0.583095189 + 0.8 = 1.383095189 x = 1.383095189 Simplifying x = 1.383095189Subproblem 2
x + -0.8 = -0.583095189 Simplifying x + -0.8 = -0.583095189 Reorder the terms: -0.8 + x = -0.583095189 Solving -0.8 + x = -0.583095189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -0.583095189 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -0.583095189 + 0.8 x = -0.583095189 + 0.8 Combine like terms: -0.583095189 + 0.8 = 0.216904811 x = 0.216904811 Simplifying x = 0.216904811Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.383095189, 0.216904811}
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