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Simplifying 0.3x + 17 = x2 + -16 Reorder the terms: 17 + 0.3x = x2 + -16 Reorder the terms: 17 + 0.3x = -16 + x2 Solving 17 + 0.3x = -16 + x2 Solving for variable 'x'. Reorder the terms: 17 + 16 + 0.3x + -1x2 = -16 + x2 + 16 + -1x2 Combine like terms: 17 + 16 = 33 33 + 0.3x + -1x2 = -16 + x2 + 16 + -1x2 Reorder the terms: 33 + 0.3x + -1x2 = -16 + 16 + x2 + -1x2 Combine like terms: -16 + 16 = 0 33 + 0.3x + -1x2 = 0 + x2 + -1x2 33 + 0.3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 33 + 0.3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -33 + -0.3x + x2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + -0.3x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + -0.3x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -0.3x + x2 = 0 + 33 -0.3x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 -0.3x + x2 = 33 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 33 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 33 + 0.0225 Combine like terms: 33 + 0.0225 = 33.0225 0.0225 + -0.3x + x2 = 33.0225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 33.0225 Calculate the square root of the right side: 5.746520686 Break this problem into two subproblems by setting (x + -0.15) equal to 5.746520686 and -5.746520686.Subproblem 1
x + -0.15 = 5.746520686 Simplifying x + -0.15 = 5.746520686 Reorder the terms: -0.15 + x = 5.746520686 Solving -0.15 + x = 5.746520686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 5.746520686 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 5.746520686 + 0.15 x = 5.746520686 + 0.15 Combine like terms: 5.746520686 + 0.15 = 5.896520686 x = 5.896520686 Simplifying x = 5.896520686Subproblem 2
x + -0.15 = -5.746520686 Simplifying x + -0.15 = -5.746520686 Reorder the terms: -0.15 + x = -5.746520686 Solving -0.15 + x = -5.746520686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -5.746520686 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -5.746520686 + 0.15 x = -5.746520686 + 0.15 Combine like terms: -5.746520686 + 0.15 = -5.596520686 x = -5.596520686 Simplifying x = -5.596520686Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.896520686, -5.596520686}
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